I am solving the code contest code and i am stuck on this problem
Calculate the number of ways to color an N * M grid using K colors.Adjacent squares in the grid should have different colors. Squares are considered adjacent if they share an edge.
Input Format
The first line contains an integer T denoting the number of test-cases.The next T lines contains integers N, M and K separated by a single space.
Sample Input
3
3 3 2
3 4 3
1 1 1
Sample Output
2
1122
1
I have attached the code in Java to solve your problem. There is not a simple formula because there are up to four squares that touch each square. This is a sample run of my program without it printing out each solution. Note that it matches the problems sample input/output.
Enter number of colors: 2
Enter number of rows: 3
Enter number of columns: 3
There are 2 different combinations of 2 colors.
Enter number of colors: 3
Enter number of rows: 4
Enter number of columns: 3
There are 1122 different combinations of 3 colors.
Enter number of colors: 1
Enter number of rows: 1
Enter number of columns: 1
There are 1 different combinations of 1 colors.
Here is the output for 3 colors, and 2 by 4 grid, printing each solution that it found. For this input, the answer is 162. For the source code, go straight to the bottom...
Enter number of colors: 3
Enter number of rows: 2
Enter number of columns: 4
1212
2121
1212
2123
1213
2121
1212
2131
1213
2131
1213
2132
1231
2123
1232
2121
1232
2123
1212
2321
1212
2323
1213
2321
1231
2312
1231
2313
1232
2313
1231
2323
1232
2321
1232
2323
1312
2121
1312
2123
1313
2121
1312
2131
1313
2131
1313
2132
1321
2132
1323
2131
1323
2132
1212
3121
1212
3123
1213
3121
1212
3131
1213
3131
1213
3132
1231
3123
1232
3121
1232
3123
1312
3121
1312
3123
1313
3121
1312
3131
1313
3131
1313
3132
1321
3132
1323
3131
1323
3132
1312
3231
1313
3231
1313
3232
1321
3212
1321
3213
1323
3212
1321
3232
1323
3231
1323
3232
2121
1212
2121
1213
2123
1212
2121
1232
2123
1231
2123
1232
2131
1212
2131
1213
2132
1213
2121
1312
2121
1313
2123
1312
2131
1312
2131
1313
2132
1313
2131
1323
2132
1321
2132
1323
2312
1231
2313
1231
2313
1232
2321
1212
2321
1213
2323
1212
2321
1232
2323
1231
2323
1232
2121
3212
2121
3213
2123
3212
2121
3232
2123
3231
2123
3232
2131
3212
2131
3213
2132
3213
2312
3121
2312
3123
2313
3121
2312
3131
2313
3131
2313
3132
2321
3132
2323
3131
2323
3132
2312
3231
2313
3231
2313
3232
2321
3212
2321
3213
2323
3212
2321
3232
2323
3231
2323
3232
3121
1212
3121
1213
3123
1212
3121
1232
3123
1231
3123
1232
3131
1212
3131
1213
3132
1213
3121
1312
3121
1313
3123
1312
3131
1312
3131
1313
3132
1313
3131
1323
3132
1321
3132
1323
3212
1321
3212
1323
3213
1321
3231
1312
3231
1313
3232
1313
3231
1323
3232
1321
3232
1323
3121
2312
3121
2313
3123
2312
3131
2312
3131
2313
3132
2313
3131
2323
3132
2321
3132
2323
3212
2121
3212
2123
3213
2121
3212
2131
3213
2131
3213
2132
3231
2123
3232
2121
3232
2123
3212
2321
3212
2323
3213
2321
3231
2312
3231
2313
3232
2313
3231
2323
3232
2321
3232
2323
There are 162 different combinations of 3 colors.
Here is the java code:
import java.util.*;
public class ColorChoices
{
int[][] grid;
int numberOfColors;
int numberOfRows;
int numberOfColumns;
int numberOfCombinations;
public static void main(String[] args)
{
ColorChoices solution = new ColorChoices();
solution.begin();
}
void begin()
{
numberOfCombinations = 0;
Scanner consoleInput = new Scanner(System.in);
System.out.print("Enter number of colors: ");
numberOfColors = consoleInput.nextInt();
System.out.print("Enter number of rows: ");
numberOfRows = consoleInput.nextInt();
System.out.print("Enter number of columns: ");
numberOfColumns = consoleInput.nextInt();
grid = new int[numberOfRows][numberOfColumns];
solve(0, 0);
System.out.println("There are " + numberOfCombinations + " different combinations of " + numberOfColors + " colors.");
}
void solve(int r, int c)
{
for(int i = 1; i <= numberOfColors; i++)
{
if(valid(r, c, i))
{
grid[r][c] = i;
if(r == numberOfRows - 1 && c == numberOfColumns - 1)
{
printBoard();
numberOfCombinations++;
}
else if(r == numberOfRows - 1) solve(0, c + 1);
else solve(r + 1, c);
}
}
grid[r][c] = 0;
}
boolean valid(int r, int c, int n)
{
return(leftOK(r, c, n) && rightOK(r, c, n) && topOK(r, c, n) && bottomOK(r, c, n));
}
boolean leftOK(int r, int c, int n)
{
if(c == 0) return true;
if(grid[r][c - 1] != n) return true;
return false;
}
boolean rightOK(int r, int c, int n)
{
if(c == numberOfColumns - 1) return true;
if(grid[r][c + 1] != n) return true;
return false;
}
boolean topOK(int r, int c, int n)
{
if(r == 0) return true;
if(grid[r - 1][c] != n) return true;
return false;
}
boolean bottomOK(int r, int c, int n)
{
if(r == numberOfRows - 1) return true;
if(grid[r + 1][c] != n) return true;
return false;
}
void printBoard()
{
for(int r = 0; r < numberOfRows; r++)
{
for(int c = 0; c < numberOfColumns; c++)
{
System.out.print(grid[r][c]);
}
System.out.println();
}
System.out.println();
}
}
Related
*edit
I have radix sort procedure, and i got this code on another site referension. But this radix sort only for ascending not for descending.
Can you guys help me how to make it to descending
Program SortStuff;
Uses Crt, Dos;
Type
AType = Array [1..400] of Integer;
Ptr = ^Node;
Node = Record
Info : Integer;
Link : Ptr;
end;
LType = Array [0..9] of Ptr;
Var
Ran : AType;
MaxData : Integer;
and this section of the procedure of refill
Procedure Refill (Var A : AType; Var L : LType);
Var
I, J : Integer;
P : Ptr;
begin
J := 1;
For I := 0 to 9 do
begin
P := L [I];
While P <> Nil do
begin
A [J] := P^.Info;
P := P^.Link;
J := J + 1;
end;
end;
For I := 0 to 9 do
L [I] := Nil;
end;
This is the radix sort code
Procedure RadixSort (Var A : AType; MaxData : Integer);
Var
L : LType;
I,
divisor,
ListNo,
Number : Integer;
begin
For I := 0 to 9 do L [I] := Nil;
divisor := 1;
While divisor <= 1000 do
begin
I := 1;
While I <= MaxData do
begin
Number := A [I];
ListNo := Number div divisor MOD 10;
Insert (L, Number, ListNo);
I := I + 1;
end;
Refill (A, L);
divisor := 10 * divisor;
end;
end;
and this the main code
begin
ReadData (Ran, MaxData);
Writeln ('Unsorted : ');
WriteArray (Ran, MaxData);
RadixSort (Ran, MaxData);
Writeln ('Sorted : ');
WriteArray (Ran, MaxData);
readln;
end.
this is the result of the compiler when ascending
Unsorted :
7131 5110 638 7836 3809 1278 9577 7590 8244 5902 7610 4787 6809 1510 3564 3358 6411 995 4966 9800 5807 678 9174 9385 4146 1824 4869 9383 3638 2304 8130 1178 5102 2192 1739 1643 2965 7245 7050 2416 3778 5515 4395 3418 4869 9814 6073 5014 8501 210 3966 4891 8992 2882 5512 3775 799 9985 8189 4664 4360 241 7681 6235 7152 8032 8874 19 9253 1943 2049 8301 1848 9175 8698 6578 8111 4442 5157 8832 9848 6448 3881 2753 4100 1130 9516 4539 5515 9756 1047 3313 2937 575 8634 9439 8508 8 2596 3814 4996 5129 9810 1220 8242 7672 7342 1320 3195 7590 4342 5697 7866 2326 6726 3441 8276 6531 2211 6285 4492 9310 2155 2349 1396 9157 772 3984 1955 9417 7644 4814 90 7922 180 6536 7018 7411 263 3775 2014 2339 4064 6623 4173 4031 5979 4930 7654 4039 1531 4916 7357 8802 6935 6108 1580 3999 6225 2641 6330 6907 2584 3437 7753 8680 2192 4461 748 983 364 1695 197 8174 3128 104 4724 546 3826 7640 8669 4481 4763 599 2983 4433 92 8317 8102 413 91 1355 7456 4577 8442 26 8319 5010 1140 1232 1688 4080 4445 3548 5713 8391 4295 296 294 1477 8487 5823 9493 4528 434 2589 9499 6092 9784 6773 1907 9382 2203 3774 8438 8672 3290 3590 4540 2912 7308 9782 5615 8352 9456 5867 5657 218 6838 6294 3295 4741 5949 9369 8949 9672 5853 7054 855 3755 3113 4712 9043 3412 4546 2567 9934 2034 2007 1845 6466 2815 3012 498 5736 2487 881 6250 780 6817 7309 8503 9697 6149 7132 6936 5692 2757 6150 2705 1401 9272 4190 6116 8096 2386 2027 8913 7734 7318 4423 8439 7087 7995 8429 7139 818 1495 3284 2418 3295 5121 2989 5741 433 1905 5468 9828 8946 3179 7615 894 9766 2971 847 6450 4686 9597 4851 2080 7062 1956 2386 7476 1703 2738 3864 6491 7545 3046 1432 1050 3534 6054 5005 4862 9126 2877 1259 8613 1209 4982 236 9877 1697 4142 7484 2562 1554 8105 6483 3440 1462 8463 2006 7193 8316 281 6544 645 7043 2857 70 5525 6953 8924 7032 7593 4514 2192 8088 59 2861 4685 897 7319 3300 410 773 2147 9992 2985 8834 302 437 4323 6566 8357 9802 8257 7543 3607 1131 564 9474 9203 9127 575 708 7767
Sorted :
8 19 26 59 70 90 91 92 104 180 197 210 218 236 241 263 281 294 296 302 364 410 413 433 434 437 498 546 564 575 575 599 638 645 678 708 748 772 773 780 799 818 847 855 881 894 897 983 995 1047 1050 1130 1131 1140 1178 1209 1220 1232 1259 1278 1320 1355 1396 1401 1432 1462 1477 1495 1510 1531 1554 1580 1643 1688 1695 1697 1703 1739 1824 1845 1848 1905 1907 1943 1955 1956 2006 2007 2014 2027 2034 2049 2080 2147 2155 2192 2192 2192 2203 2211 2304 2326 2339 2349 2386 2386 2416 2418 2487 2562 2567 2584 2589 2596 2641 2705 2738 2753 2757 2815 2857 2861 2877 2882 2912 2937 2965 2971 2983 2985 2989 3012 3046 3113 3128 3179 3195 3284 3290 3295 3295 3300 3313 3358 3412 3418 3437 3440 3441 3534 3548 3564 3590 3607 3638 3755 3774 3775 3775 3778 3809 3814 3826 3864 3881 3966 3984 3999 4031 4039 4064 4080 4100 4142 4146 4173 4190 4295 4323 4342 4360 4395 4423 4433 4442 4445 4461 4481 4492 4514 4528 4539 4540 4546 4577 4664 4685 4686 4712 4724 4741 4763 4787 4814 4851 4862 4869 4869 4891 4916 4930 4966 4982 4996 5005 5010 5014 5102 5110 5121 5129 5157 5468 5512 5515 5515 5525 5615 5657 5692 5697 5713 5736 5741 5807 5823 5853 5867 5902 5949 5979 6054 6073 6092 6108 6116 6149 6150 6225 6235 6250 6285 6294 6330 6411 6448 6450 6466 6483 6491 6531 6536 6544 6566 6578 6623 6726 6773 6809 6817 6838 6907 6935 6936 6953 7018 7032 7043 7050 7054 7062 7087 7131 7132 7139 7152 7193 7245 7308 7309 7318 7319 7342 7357 7411 7456 7476 7484 7543 7545 7590 7590 7593 7610 7615 7640 7644 7654 7672 7681 7734 7753 7767 7836 7866 7922 7995 8032 8088 8096 8102 8105 8111 8130 8174 8189 8242 8244 8257 8276 8301 8316 8317 8319 8352 8357 8391 8429 8438 8439 8442 8463 8487 8501 8503 8508 8613 8634 8669 8672 8680 8698 8802 8832 8834 8874 8913 8924 8946 8949 8992 9043 9126 9127 9157 9174 9175 9203 9253 9272 9310 9369 9382 9383 9385 9417 9439 9456 9474 9493 9499 9516 9577 9597 9672 9697 9756 9766 9782 9784 9800 9802 9810 9814 9828 9848 9877 9934 9985 9992
then i tried to modify ListNo := Number div divisor MOD 10; and reverse it into ListNo := divisor div Number MOD 10; and the final result become to
Unsorted :
7131 5110 638 7836 3809 1278 9577 7590 8244 5902 7610 4787 6809 1510 3564 3358 6411 995 4966 9800 5807 678 9174 9385 4146 1824 4869 9383 3638 2304 8130 1178 5102 2192 1739 1643 2965 7245 7050 2416 3778 5515 4395 3418 4869 9814 6073 5014 8501 210 3966 4891 8992 2882 5512 3775 799 9985 8189 4664 4360 241 7681 6235 7152 8032 8874 19 9253 1943 2049 8301 1848 9175 8698 6578 8111 4442 5157 8832 9848 6448 3881 2753 4100 1130 9516 4539 5515 9756 1047 3313 2937 575 8634 9439 8508 8 2596 3814 4996 5129 9810 1220 8242 7672 7342 1320 3195 7590 4342 5697 7866 2326 6726 3441 8276 6531 2211 6285 4492 9310 2155 2349 1396 9157 772 3984 1955 9417 7644 4814 90 7922 180 6536 7018 7411 263 3775 2014 2339 4064 6623 4173 4031 5979 4930 7654 4039 1531 4916 7357 8802 6935 6108 1580 3999 6225 2641 6330 6907 2584 3437 7753 8680 2192 4461 748 983 364 1695 197 8174 3128 104 4724 546 3826 7640 8669 4481 4763 599 2983 4433 92 8317 8102 413 91 1355 7456 4577 8442 26 8319 5010 1140 1232 1688 4080 4445 3548 5713 8391 4295 296 294 1477 8487 5823 9493 4528 434 2589 9499 6092 9784 6773 1907 9382 2203 3774 8438 8672 3290 3590 4540 2912 7308 9782 5615 8352 9456 5867 5657 218 6838 6294 3295 4741 5949 9369 8949 9672 5853 7054 855 3755 3113 4712 9043 3412 4546 2567 9934 2034 2007 1845 6466 2815 3012 498 5736 2487 881 6250 780 6817 7309 8503 9697 6149 7132 6936 5692 2757 6150 2705 1401 9272 4190 6116 8096 2386 2027 8913 7734 7318 4423 8439 7087 7995 8429 7139 818 1495 3284 2418 3295 5121 2989 5741 433 1905 5468 9828 8946 3179 7615 894 9766 2971 847 6450 4686 9597 4851 2080 7062 1956 2386 7476 1703 2738 3864 6491 7545 3046 1432 1050 3534 6054 5005 4862 9126 2877 1259 8613 1209 4982 236 9877 1697 4142 7484 2562 1554 8105 6483 3440 1462 8463 2006 7193 8316 281 6544 645 7043 2857 70 5525 6953 8924 7032 7593 4514 2192 8088 59 2861 4685 897 7319 3300 410 773 2147 9992 2985 8834 302 437 4323 6566 8357 9802 8257 7543 3607 1131 564 9474 9203 9127 575 708 7767
Sorted :
7131 5110 7836 3809 1278 9577 7590 8244 5902 7610 4787 6809 1510 3564 3358 6411 4966 9800 5807 9174 9385 4146 1824 4869 9383 3638 2304 8130 1178 5102 2192 1739 1643 2965 7245 7050 2416 3778 5515 4395 3418 4869 9814 6073 5014 8501 3966 4891 8992 2882 5512 3775 9985 8189 4664 4360 7681 6235 7152 8032 8874 9253 1943 2049 8301 1848 9175 8698 6578 8111 4442 5157 8832 9848 6448 3881 2753 4100 1130 9516 4539 5515 9756 1047 3313 2937 8634 9439 8508 2596 3814 4996 5129 9810 1220 8242 7672 7342 1320 3195 7590 4342 5697 7866 2326 6726 3441 8276 6531 2211 6285 4492 9310 2155 2349 1396 9157 3984 1955 9417 7644 4814 7922 6536 7018 7411 3775 2014 2339 4064 6623 4173 4031 5979 4930 7654 4039 1531 4916 7357 8802 6935 6108 1580 3999 6225 2641 6330 6907 2584 3437 7753 8680 2192 4461 1695 8174 3128 4724 3826 7640 8669 4481 4763 2983 4433 8317 8102 1355 7456 4577 8442 8319 5010 1140 1232 1688 4080 4445 3548 5713 8391 4295 1477 8487 5823 9493 4528 2589 9499 6092 9784 6773 1907 9382 2203 3774 8438 8672 3290 3590 4540 2912 7308 9782 5615 8352 9456 5867 5657 6838 6294 3295 4741 5949 9369 8949 9672 5853 7054 3755 3113 4712 9043 3412 4546 2567 9934 2034 2007 1845 6466 2815 3012 5736 2487 6250 6817 7309 8503 9697 6149 7132 6936 5692 2757 6150 2705 1401 9272 4190 6116 8096 2386 2027 8913 7734 7318 4423 8439 7087 7995 8429 7139 1495 3284 2418 3295 5121 2989 5741 1905 5468 9828 8946 3179 7615 9766 2971 6450 4686 9597 4851 2080 7062 1956 2386 7476 1703 2738 3864 6491 7545 3046 1432 1050 3534 6054 5005 4862 9126 2877 1259 8613 1209 4982 9877 1697 4142 7484 2562 1554 8105 6483 3440 1462 8463 2006 7193 8316 6544 7043 2857 5525 6953 8924 7032 7593 4514 2192 8088 2861 4685 7319 3300 2147 9992 2985 8834 4323 6566 8357 9802 8257 7543 3607 1131 9474 9203 9127 7767 92 91 638 995 678 799 575 772 748 983 546 599 855 881 780 818 894 847 645 897 773 564 575 708 90 364 413 434 498 433 410 437 19 263 296 294 281 302 210 241 218 236 70 180 197 8 59 26 104
I was trying to read firmware from a NAND chip, and extract its program and data for analyse.
From online I learned, you must create an UBI device with your image file write to it, then you can mount it to your system.
Description
First I read a bin file from FLASH chip. binwalk I get this.
$ binwalk -Me Flash_data.bin
DECIMAL HEXADECIMAL DESCRIPTION
--------------------------------------------------------------------------------
771180 0xBC46C device tree image (dtb)
772444 0xBC95C device tree image (dtb)
823236 0xC8FC4 CRC32 polynomial table, little endian
2703360 0x294000 uImage header, header size: 64 bytes, header CRC: 0xF092DEF5, created: 2016-10-04 21:32:58, image size: 2773040 bytes, Data Address: 0x80008000, Entry Point: 0x80008000, data CRC: 0x365DF8B1, OS: Linux, CPU: ARM, image type: OS Kernel Image, compression type: none, image name: "Linux-3.2.0"
2703424 0x294040 Linux kernel ARM boot executable zImage (little-endian)
2722452 0x298A94 gzip compressed data, maximum compression, from Unix, last modified: 1970-01-01 00:00:00 (null date)
8110080 0x7BC000 UBI erase count header, version: 1, EC: 0x2, VID header offset: 0x800, data offset: 0x1000
From its output files, I foun this ubi image file.
$ binwalk 7BC000.ubi
DECIMAL HEXADECIMAL DESCRIPTION
--------------------------------------------------------------------------------
0 0x0 UBI erase count header, version: 1, EC: 0x2, VID header offset: 0x800, data offset: 0x1000
$ file 7BC000.ubi
7BC000.ubi: UBI image, version 1
Some information about NAND chip:
PageSize : 2048
SpareSize : 64
PagesPerBlock : 64
Blocks Size : 128KB + 4KB
Total Block : 2048
Device Size : 256MB + 8192KB8192KB
Bus Width : 8
Then I tried to mount it, like this:
$ sudo modprobe mtdblock
$ sudo modprobe nandsim first_id_byte=0x20 second_id_byte=0xac third_id_byte=0x00 fourth_id_byte=0x15
$ mtdinfo /dev/mtd0
mtd0
Name: NAND simulator partition 0
Type: nand
Eraseblock size: 131072 bytes, 128.0 KiB
Amount of eraseblocks: 4096 (536870912 bytes, 512.0 MiB)
Minimum input/output unit size: 2048 bytes
Sub-page size: 512 bytes
OOB size: 64 bytes
Character device major/minor: 90:0
Bad blocks are allowed: true
Device is writable: true
$ sudo flash_erase /dev/mtd0 0 0
$ cp 7BC000.ubi test_infile
$ sudo ubiformat /dev/mtd0 -O 2048 -f test_infile
ubiformat: mtd0 (nand), size 536870912 bytes (512.0 MiB), 4096 eraseblocks of 131072 bytes (128.0 KiB), min. I/O size 2048 bytes
libscan: scanning eraseblock 4095 -- 100 % complete
ubiformat: 4096 eraseblocks are supposedly empty
ubiformat: error!: file "test_infile" (size 268713984 bytes) is not multiple of eraseblock size (131072 bytes)
error 0 (Success)
The size of "test_file" is 0x10044000, so I just remove the last 0x4000 bytes, and tried to ubiformat again.
$ dd if=test_infile of=test_infile_dd bs=268697600 count=1
$ sudo ubiformat /dev/mtd0 -O 2048 -f test_infile_dd
ubiformat: mtd0 (nand), size 536870912 bytes (512.0 MiB), 4096 eraseblocks of 131072 bytes (128.0 KiB), min. I/O size 2048 bytes
libscan: scanning eraseblock 4095 -- 100 % complete
ubiformat: 4096 eraseblocks are supposedly empty
ubiformat: flashing eraseblock 1 -- 0 % complete ubiformat: error!: bad UBI magic 0xffffffff, should be 0x55424923
ubiformat: error!: bad EC header at eraseblock 1 of "test_infile_dd"
I did some research and found out, in this UBI image, there are many blocks, and every block contains data and OOB.
The reason last command fails because it searchs 0x55424923 at wrong position which is 0x20000, because of OOB, 0x55424923 is actually at 0x21000, so I think perhaps delete all of OOB part from "this_file_dd" might work. The bash command and test as follows.
#!/bin/bash
# ./dump.sh
# pagesize 0x20000
# oob size 0x01000
# block 1
dd if=infile of=test_infile_dd_nooob bs=$((0x20000)) count=1
declare -i i=1
# block others
while ((i<2048))
do
dd if=test_infile of=out bs=$((0x21000)) count=1 skip=$i
dd if=out of=outfile bs=$((0x20000)) count=1
cat outfile >> test_infile_dd_nooob
rm out
rm outfile
let i++
done
After remove all OOB, compare 2 file, and noticed that OOB has been remove.
$ xxd test_infile_dd | grep "5542 4923" ⏎
00000000: 5542 4923 0100 0000 0000 0000 0000 0002 UBI#............
00021000: 5542 4923 0100 0000 0000 0000 0000 0002 UBI#............
00042000: 5542 4923 0100 0000 0000 0000 0000 0001 UBI#............
00063000: 5542 4923 0100 0000 0000 0000 0000 0001 UBI#............
00084000: 5542 4923 0100 0000 0000 0000 0000 0001 UBI#............
$ xxd test_infile_dd_nooob | grep "5542 4923"
00000000: 5542 4923 0100 0000 0000 0000 0000 0002 UBI#............
00020000: 5542 4923 0100 0000 0000 0000 0000 0002 UBI#............
00040000: 5542 4923 0100 0000 0000 0000 0000 0001 UBI#............
00060000: 5542 4923 0100 0000 0000 0000 0000 0001 UBI#............
00080000: 5542 4923 0100 0000 0000 0000 0000 0001 UBI#............
Then ubiformat again, another error about bad UBI magic.
$ sudo ubiformat /dev/mtd0 -O 2048 -f test_infile_dd_nooob
ubiformat: mtd0 (nand), size 536870912 bytes (512.0 MiB), 4096 eraseblocks of 131072 bytes (128.0 KiB), min. I/O size 2048 bytes
libscan: scanning eraseblock 4095 -- 100 % complete
ubiformat: 1 eraseblocks have valid erase counter, mean value is 0
ubiformat: 4095 eraseblocks are supposedly empty
ubiformat: warning!: only 1 of 4096 eraseblocks have valid erase counter
ubiformat: erase counter 0 will be used for all eraseblocks
ubiformat: note, arbitrary erase counter value may be specified using -e option
ubiformat: continue? (y/N) y
ubiformat: use erase counter 0 for all eraseblocks
ubiformat: flashing eraseblock 1074 -- 54 % complete ubiformat: error!: bad UBI magic 00000000, should be 0x55424923
ubiformat: error!: bad EC header at eraseblock 1074 of "test_infile_dd_nooob"
Used ghex to fix wrong EC header in EB-1074, and ubiformat again, same block's CRC is not right.
sudo ubiformat /dev/mtd0 -O 2048 -f test_infile_dd_nooob -e 10
ubiformat: mtd0 (nand), size 536870912 bytes (512.0 MiB), 4096 eraseblocks of 131072 bytes (128.0 KiB), min. I/O size 2048 bytes
libscan: scanning eraseblock 4095 -- 100 % complete
ubiformat: 1074 eraseblocks have valid erase counter, mean value is 10
ubiformat: 3022 eraseblocks are supposedly empty
ubiformat: use erase counter 10 for all eraseblocks
ubiformat: flashing eraseblock 1074 -- 54 % complete ubiformat: error!: bad CRC 0x7d72af58, should be 00000000
ubiformat: error!: bad EC header at eraseblock 1074 of "test_infile_dd_nooob"
Fix CRC and ubiformat again, enable ubi and ubiattach to mtd0, but another error occurs.
sudo ubiformat /dev/mtd0 -O 2048 -f test_infile_dd_nooob -e 10 ⏎
ubiformat: mtd0 (nand), size 536870912 bytes (512.0 MiB), 4096 eraseblocks of 131072 bytes (128.0 KiB), min. I/O size 2048 bytes
libscan: scanning eraseblock 4095 -- 100 % complete
ubiformat: 1074 eraseblocks have valid erase counter, mean value is 10
ubiformat: 3022 eraseblocks are supposedly empty
ubiformat: use erase counter 10 for all eraseblocks
ubiformat: flashing eraseblock 1987 -- 100 % complete
ubiformat: formatting eraseblock 4095 -- 100 % complete
$ sudo modprobe ubi
$ sudo modprobe ubi mtd=0
$ sudo ubiattach -m 0 -O 2048
ubiattach: error!: cannot attach mtd0
error 22 (Invalid argument)
Do dmesg I found this message.
$ sudo dmesg
[ 6974.021149] 0001efa0: 00 00 00 00 00 00 00 00 10 0a 00 00 01 00 00 00 00 0a d9 d5 05 f9 20 a1 63 d7 00 00 00 02 fb d2 ...................... .c.......
[ 6974.021150] 0001efc0: ce 15 00 00 00 0d 00 00 02 00 00 00 04 00 20 00 c7 00 00 00 0d 0d 0d 00 00 00 0b 01 b8 00 03 db .............. .................
[ 6974.021151] 0001efe0: 03 9d 03 5e 03 20 02 fd 02 d8 02 93 02 4e 02 1b 01 f6 01 b8 20 00 7a 14 08 00 32 3b 81 0e 04 17 ...^. .......N...... .z...2;....
[ 6974.023703] ubi0 error: validate_ec_hdr [ubi]: node with incompatible UBI version found: this UBI version is 1, image version is 0
[ 6974.023707] ubi0 error: validate_ec_hdr [ubi]: bad EC header
[ 6974.023707] Erase counter header dump:
[ 6974.023708] magic 0x55424923
[ 6974.023708] version 0
[ 6974.023709] ec 10
[ 6974.023709] vid_hdr_offset 2048
[ 6974.023710] data_offset 4096
[ 6974.023710] image_seq 144665903
[ 6974.023711] hdr_crc 0xb574c34c
[ 6974.023711] erase counter header hexdump:
[ 6974.023713] 00000000: 55 42 49 23 00 00 00 00 00 00 00 00 00 00 00 0a 00 00 08 00 00 00 10 00 08 9f 6d 2f 00 00 00 00 UBI#......................m/....
[ 6974.023713] 00000020: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 b5 74 c3 4c .............................t.L
[ 6974.023715] CPU: 4 PID: 14955 Comm: ubiattach Tainted: G W E 5.7.0-kali1-amd64 #1 Debian 5.7.6-1kali2
[ 6974.023716] Hardware name: Dell Inc. Inspiron 7472/0GHVRJ, BIOS 1.1.6 06/14/2018
[ 6974.023716] Call Trace:
[ 6974.023722] dump_stack+0x66/0x90
[ 6974.023725] validate_ec_hdr+0x8a/0xe0 [ubi]
[ 6974.023729] ubi_io_read_ec_hdr+0x1e9/0x280 [ubi]
[ 6974.023732] ubi_attach+0x1d3/0x14c0 [ubi]
[ 6974.023736] ubi_attach_mtd_dev+0x5b3/0xd30 [ubi]
[ 6974.023741] ? __get_mtd_device+0x2c/0xa0 [mtd]
[ 6974.023743] ? _cond_resched+0x15/0x30
[ 6974.023746] ctrl_cdev_ioctl+0xda/0x1c0 [ubi]
[ 6974.023748] ksys_ioctl+0x87/0xc0
[ 6974.023749] __x64_sys_ioctl+0x16/0x20
[ 6974.023751] do_syscall_64+0x52/0x180
[ 6974.023753] entry_SYSCALL_64_after_hwframe+0x44/0xa9
[ 6974.023754] RIP: 0033:0x7f3f55902c87
[ 6974.023756] Code: 00 00 00 48 8b 05 09 92 0c 00 64 c7 00 26 00 00 00 48 c7 c0 ff ff ff ff c3 66 2e 0f 1f 84 00 00 00 00 00 b8 10 00 00 00 0f 05 <48> 3d 01 f0 ff ff 73 01 c3 48 8b 0d d9 91 0c 00 f7 d8 64 89 01 48
[ 6974.023756] RSP: 002b:00007ffd4fec6f88 EFLAGS: 00000206 ORIG_RAX: 0000000000000010
[ 6974.023757] RAX: ffffffffffffffda RBX: 00007ffd4fec7020 RCX: 00007f3f55902c87
[ 6974.023758] RDX: 00007ffd4fec6fb0 RSI: 0000000040186f40 RDI: 0000000000000003
[ 6974.023758] RBP: 0000000000000003 R08: 0000000000000001 R09: 0000000000000000
[ 6974.023759] R10: fffffffffffff48e R11: 0000000000000206 R12: 000055c2a393c052
[ 6974.023759] R13: 00007ffd4fec6fb0 R14: 0000000000000000 R15: 0000000000000000
[ 6974.023763] ubi0 error: ubi_io_read_ec_hdr [ubi]: validation failed for PEB 1074
[ 6974.061006] ubi0 error: ubi_attach_mtd_dev [ubi]: failed to attach mtd0, error -22
But I don't know how to solve this, so I just remove block 1074 from file.
$ dd if=test_infile_dd_nooob of=test_infile_dd_nooob_no1074_1 bs=131072 count=1074
$ dd if=test_infile_dd_nooob of=test_infile_dd_nooob_no1074_2 bs=131072 skip=1075
$ cat test_infile_dd_nooob_no1074_1 test_infile_dd_nooob_no1074_2 > test_infile_dd_nooob_no1074
Then ubiformat and attach again, but there was another error.
$ sudo ubiformat /dev/mtd0 -O 2048 -f test_infile_dd_nooob_no1074 -e 10
ubiformat: mtd0 (nand), size 536870912 bytes (512.0 MiB), 4096 eraseblocks of 131072 bytes (128.0 KiB), min. I/O size 2048 bytes
libscan: scanning eraseblock 4095 -- 100 % complete
ubiformat: 4096 eraseblocks have valid erase counter, mean value is 10
ubiformat: use erase counter 10 for all eraseblocks
ubiformat: flashing eraseblock 1986 -- 100 % complete
ubiformat: formatting eraseblock 4095 -- 100 % complete
$ sudo ubiattach -m 0 -O 2048 ⏎
ubiattach: error!: cannot attach mtd0
error 22 (Invalid argument)
Check dmesg and found this, this is where I don't know how to do, I don't know how I get so many bad blocks.
$ sudo dmesg
ubi0: scanning is finished
[ 7392.005554] ubi0 error: ubi_attach [ubi]: 1205 PEBs are corrupted and preserved
[ 7392.005554] Corrupted PEBs are: 1805 1802 1793 1678 1674 1670 1666 1662 1654 1653 1652 1649 1640 1639 1626 1625 1621 1605 1587 1586 1581 1563 1553 1540 1534 1533 1532 1531 1530 1529 1528 1527 1526 1525 1524 1523 1522 1521 1520 1519 1518 1517 1516 1515 1514 1512 1511 1510 1509 1508 1507 1506 1505 1504 1503 1502 1501 1500 1499 1498 1496 1495 1494 1493 1492 1491 1490 1489 1488 1487 1486 1485 1484 1483 1482 1481 1471 1449 1448 1447 1446 1445 1444 1441 1439 1438 1437 1436 1435 1434 1433 1432 1431 1430 1429 1428 1425 1424 1423 1422 1421 1420 1419 1418 1417 1416 1415 1414 1413 1412 1411 1410 1409 1408 1407 1406 1405 1404 1403 1402 1401 1400 1399 1398 1397 1396 1395 1394 1393 1391 1390 1389 1388 1387 1386 1385 1384 1383 1382 1381 1380 1379 1378 1377 1376 1375 1374 1373 1372 1371 1370 1369 1368 1367 1366 1365 1364 1363 1362 1361 1360 1359 1358 1357 1356 1355 1354 1353 1352 1351 1350 1349 1348 1347 1346 1345 1344 1343 1342 1341 1340 1339 1338 1337 1335 1334 1333 1332 1331 1330 1329 1328 1327 1326
[ 7392.005578] 1325 1324 1323 1322 1321 1294 1275 1274 1273 1264 1230 1223 1221 1219 1214 1211 1210 1207 1204 1203 1202 1201 1200 1199 1198 1197 1196 1195 1194 1193 1192 1191 1190 1189 1188 1187 1186 1185 1184 1183 1182 1181 1180 1179 1178 1177 1176 1175 1174 1173 1172 1165 1164 1163 1157 1147 1144 1143 1142 1141 1140 1139 1138 1137 1136 1134 1133 1132 1131 1130 1129 1128 1127 1126 1125 1124 1123 1122 1121 1120 1119 1118 1117 1116 1115 1114 1112 1111 1110 1109 1108 1106 1105 1098 1085 1053 1052 1044 1016 1003 1002 977 973 972 963 939 938 937 936 935 934 933 932 931 930 929 928 927 926 925 924 923 922 921 920 919 918 917 916 915 914 913 912 911 910 909 908 907 906 905 904 903 902 900 899 898 897 896 895 894 893 892 891 890 889 888 887 886 885 884 883 882 881 880 879 878 877 876 875 874 873 872 871 870 869 868 867 866 865 864 863 862 861 860 859 858 857 856 855 854 853 852 851 850 849 848 847 846 845 844 841 840 839 838 837 836 835 834 833 832 831 830 829 828 827 826 825 824 823 822 821 820
[ 7392.005606] 819 818 817 816 815 814 813 812 811 810 809 808 807 806 805 804 803 802 801 800 799 798 797 796 795 794 793 792 791 790 789 788 787 785 784 782 781 780 779 778 777 776 775 774 773 772 771 770 769 768 767 766 765 764 763 762 761 760 759 758 757 756 755 754 753 752 751 750 749 748 747 746 745 744 743 742 741 740 739 738 737 736 735 734 733 732 731 730 729 727 726 725 724 723 722 721 720 719 718 716 715 714 713 712 711 710 709 708 707 706 705 704 703 702 701 700 699 698 697 696 695 694 693 692 691 690 689 688 687 686 685 684 683 682 681 680 679 678 677 676 675 674 673 672 671 670 668 667 666 665 664 663 662 661 660 659 657 656 655 654 653 652 651 650 649 648 647 646 645 644 643 642 641 640 639 638 637 636 635 634 633 632 631 630 629 628 627 626 625 624 623 622 621 620 619 618 617 616 615 614 613 611 610 609 608 607 606 605 604 602 601 600 599 598 597 596 595 594 593 592 591 589 588 587 586 585 584 583 582 581 580 579 578 577 576 575 574 573 572 571 570 569 568 567 566 565 564 563
[ 7392.005634] 562 561 560 559 558 557 556 554 553 552 551 550 549 548 547 546 545 544 543 541 540 539 538 537 536 535 534 533 532 531 530 529 528 527 526 525 524 523 522 521 520 519 518 517 516 515 514 513 512 511 510 509 508 507 506 505 504 503 502 501 500 498 497 496 495 494 493 492 491 489 488 487 486 485 484 483 482 481 480 479 478 477 476 475 474 473 472 471 470 469 468 467 466 465 464 463 461 460 459 458 457 456 455 454 453 452 451 450 449 448 447 446 445 444 443 441 440 438 437 436 435 434 433 432 431 430 429 428 427 426 425 424 423 422 421 420 419 418 417 416 415 414 413 412 411 410 409 408 407 406 405 404 403 402 401 400 399 398 397 396 395 394 393 392 391 390 389 388 387 386 384 383 382 381 380 379 378 377 376 375 374 373 372 371 370 369 368 367 366 365 364 363 362 361 360 359 358 357 356 355 354 353 352 351 350 349 348 347 346 345 344 343 342 341 340 339 338 337 336 335 333 332 331 330 329 328 327 326 325 324 323 322 321 320 319 318 317 316 315 314 313 312 311 310 309 308 307 306
[ 7392.005661] 305 304 303 302 301 300 295 294 293 292 290 289 288 287 286 285 284 283 282 281 280 279 278 277 276 275 274 273 271 270 269 268 267 266 265 264 263 262 261 260 259 258 257 256 255 254 253 252 251 250 249 248 247 246 245 244 243 242 241 240 239 238 237 236 235 233 231 230 229 228 227 226 225 224 223 222 221 220 219 218 217 216 215 214 213 212 211 210 209 208 207 206 205 204 203 202 201 200 199 198 197 196 195 194 193 192 191 190 189 188 187 186 185 184 183 182 181 180 179 177 176 175 174 172 171 170 169 168 167 166 165 164 163 162 161 160 159 158 157 156 155 154 153 152 151 150 149 148 147 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131 130 129 128 127 126 125 124 123 122 121 120 118 117 116 115 114 113 112 111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30
[ 7392.005690] 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2
[ 7392.005698] ubi0 error: ubi_attach.cold [ubi]: too many corrupted PEBs, refusing
[ 7392.028819] ubi0 error: ubi_attach_mtd_dev [ubi]: failed to attach mtd0, error -22
[ 7393.182325] systemd-journald[331]: /dev/kmsg buffer overrun, some messages lost.
I read the official documents, it says only in 2 senerios a block will be marked as bad. One is
when write opertion to eraseblock fails, UBI will move data from bad EB to a good EB, and do some tests so it can confirm whether bad EB is really bad; or when erase opertion have EIO error, then EB will be marked as bad block immediately. I am not sure which reason caused so much bad block.
My questions
In the progess, is my command doing wrong? If not, how to repair this UBI image so I can read its programs and data?
Is there other ways that can get programs and data from this UBI image file?
Tools and versions
Kali 2020.3
mtd-utils 2.1.1
I'm trying to generate a zobrist key for transposition tables in my chess engine.
Here's how I'm generating the 64 bit numbers,
as show here: How to generate 64 bit random numbers?
typedef unsigned long long U64;
std::random_device rd;
std::mt19937_64 mt(rd());
std::uniform_int_distribution<U64> dist(std::llround(std::pow(2,61)),
std::llround(std::pow(2,62)));
rand function:
U64 ZobristH::random64()
{
U64 ranUI = dist(mt);
return ranUI;
}
In order to try and make sure i'm generating random enough numbers I'm using a test distribution function I found online that looks like this (will later input data into excel and look at distribution):
int sampleSize = 2000;
int distArray[sampleSize];
int t = 0;
while (t < 10)
{
for (int i = 0; i < 10000; i++)
{
distArray[(int)(random64() % (sampleSize / 2))]++;
}
t++;
}
for (int i = 0; i < sampleSize; i++)
{
std::cout << distArray[i] << ", ";
}
the results I'm getting look a little something like this:
416763345, 417123246, 7913280, 7914356, 417726722, 417726718, 19, 83886102,
77332499, 14
Are these the decimal representation of binary numbers below 1000? Or am I doing something completely wrong?
Okay I did this to check out the distribution of random numbers; you can run this short program to generate a text file to look to see what values you are getting. Instead of using a function call I just used a lambda within the for loop and instead of setting the values into the array I wrote the values out to the text file before and after the post increment.
#include <iostream>
#include <fstream>
#include <iomanip>
#include <random>
#include <functional> // may not need - included in almost all of my apps
#include <algorithm> // same as above
typedef unsigned long long U64;
int main( int argc, char** argv ) {
std::random_device rd;
std::mt19937_64 mt( rd() );
std::uniform_int_distribution<U64> dist( std::llround( std::pow( 2, 61 ) ),
std::llround( std::pow( 2, 62 ) ) );
auto lambda = [&] { return dist(mt); };
const int sampleSize = 2000;
// int distArray[sampleSize];
int t = 0;
std::ofstream file( "samples.txt" );
while ( t < 10 ) {
file << "Sample: " << (t+1) << "\n";
for ( int i = 0; i < 10000; i++ ) {
auto val = static_cast<int>( (lambda() % (sampleSize / 2)) );
file << std::setw(5) << i << ": " << std::setw(6) << val << "\t"
<< std::setw(6) << val++ << "\n";
// distArray[...]
}
file << "\n\n";
t++;
}
file.close();
/* for ( int i = 0; i < sampleSize; i++ ) {
std::cout << distArray[i] << "\n";
}*/
// Quick & Dirty Way TO Pause The Console
std::cout << "\nPress any key and enter to quit.\n";
char c;
std::cin >> c;
return 0;
}
Then check out the text file that this program generates and if you scroll through the file you will see the distributions. The first column is the value before the post increment and the second column is after. The largest possible value before the post increment that I have seen is 1,000 and after the post increment is 999. I've built and ran this for both 32 & 64 bit platform versions and have seen similar results for the distributions and that they indeed have a uniform distribution.
Sample.txt - Small Version About 1,000 Entries Out The 1st Sample Set
Sample: 1
0: 342 341
1: 517 516
2: 402 401
3: 741 740
4: 238 237
5: 557 556
6: 35 34
7: 572 571
8: 205 204
9: 353 352
10: 301 300
11: 65 64
12: 223 222
13: 647 646
14: 185 184
15: 535 534
16: 97 96
17: 843 842
18: 716 715
19: 294 293
20: 485 484
21: 648 647
22: 406 405
23: 250 249
24: 245 244
25: 915 914
26: 888 887
27: 986 985
28: 345 344
29: 493 492
30: 654 653
31: 860 859
32: 921 920
33: 526 525
34: 793 792
35: 503 502
36: 939 938
37: 802 801
38: 142 141
39: 806 805
40: 540 539
41: 778 777
42: 787 786
43: 884 883
44: 109 108
45: 842 841
46: 794 793
47: 279 278
48: 821 820
49: 112 111
50: 438 437
51: 402 401
52: 69 68
53: 396 395
54: 196 195
55: 655 654
56: 859 858
57: 674 673
58: 417 416
59: 331 330
60: 632 631
61: 210 209
62: 641 640
63: 737 736
64: 838 837
65: 592 591
66: 562 561
67: 883 882
68: 750 749
69: 726 725
70: 253 252
71: 660 659
72: 57 56
73: 401 400
74: 919 918
75: 851 850
76: 345 344
77: 25 24
78: 300 299
79: 781 780
80: 695 694
81: 220 219
82: 378 377
83: 471 470
84: 281 280
85: 945 944
86: 536 535
87: 407 406
88: 431 430
89: 745 744
90: 32 31
91: 389 388
92: 358 357
93: 582 581
94: 820 819
95: 622 621
96: 459 458
97: 233 232
98: 594 593
99: 509 508
100: 260 259
101: 152 151
102: 148 147
103: 137 136
104: 945 944
105: 244 243
106: 968 967
107: 54 53
108: 420 419
109: 58 57
110: 678 677
111: 715 714
112: 780 779
113: 834 833
114: 241 240
115: 669 668
116: 722 721
117: 608 607
118: 805 804
119: 155 154
120: 220 219
121: 520 519
122: 740 739
123: 184 183
124: 198 197
125: 247 246
126: 115 114
127: 520 519
128: 457 456
129: 864 863
130: 659 658
131: 511 510
132: 718 717
133: 119 118
134: 588 587
135: 113 112
136: 518 517
137: 164 163
138: 375 374
139: 866 865
140: 382 381
141: 526 525
142: 621 620
143: 680 679
144: 147 146
145: 712 711
146: 408 407
147: 486 485
148: 7 6
149: 203 202
150: 741 740
151: 290 289
152: 810 809
153: 960 959
154: 449 448
155: 683 682
156: 997 996
157: 454 453
158: 131 130
159: 427 426
160: 157 156
161: 3 2
162: 427 426
163: 554 553
164: 806 805
165: 228 227
166: 431 430
167: 174 173
168: 845 844
169: 121 120
170: 397 396
171: 770 769
172: 17 16
173: 761 760
174: 736 735
175: 629 628
176: 772 771
177: 417 416
178: 739 738
179: 226 225
180: 301 300
181: 217 216
182: 746 745
183: 344 343
184: 607 606
185: 927 926
186: 428 427
187: 385 384
188: 287 286
189: 537 536
190: 705 704
191: 649 648
192: 127 126
193: 252 251
194: 160 159
195: 390 389
196: 282 281
197: 66 65
198: 659 658
199: 844 843
200: 358 357
201: 360 359
202: 872 871
203: 495 494
204: 695 694
205: 988 987
206: 969 968
207: 641 640
208: 799 798
209: 30 29
210: 109 108
211: 675 674
212: 345 344
213: 309 308
214: 807 806
215: 283 282
216: 457 456
217: 193 192
218: 972 971
219: 330 329
220: 914 913
221: 508 507
222: 624 623
223: 254 253
224: 342 341
225: 69 68
226: 918 917
227: 551 550
228: 148 147
229: 645 644
230: 905 904
231: 503 502
232: 980 979
233: 881 880
234: 137 136
235: 202 201
236: 808 807
237: 988 987
238: 497 496
239: 506 505
240: 576 575
241: 671 670
242: 874 873
243: 217 216
244: 808 807
245: 741 740
246: 14 13
247: 206 205
248: 894 893
249: 180 179
250: 4 3
251: 27 26
252: 62 61
253: 203 202
254: 392 391
255: 868 867
256: 673 672
257: 881 880
258: 664 663
259: 831 830
260: 293 292
261: 916 915
262: 860 859
263: 487 486
264: 642 641
265: 161 160
266: 881 880
267: 233 232
268: 423 422
269: 12 11
270: 398 397
271: 993 992
272: 323 322
273: 878 877
274: 114 113
275: 42 41
276: 58 57
277: 398 397
278: 878 877
279: 64 63
280: 873 872
281: 841 840
282: 506 505
283: 412 411
284: 545 544
285: 887 886
286: 17 16
287: 504 503
288: 350 349
289: 772 771
290: 16 15
291: 597 596
292: 553 552
293: 25 24
294: 324 323
295: 242 241
296: 580 579
297: 479 478
298: 702 701
299: 640 639
300: 173 172
301: 918 917
302: 678 677
303: 714 713
304: 258 257
305: 97 96
306: 304 303
307: 80 79
308: 394 393
309: 940 939
310: 985 984
311: 651 650
312: 42 41
313: 179 178
314: 672 671
315: 915 914
316: 160 159
317: 332 331
318: 887 886
319: 370 369
320: 850 849
321: 730 729
322: 395 394
323: 889 888
324: 114 113
325: 505 504
326: 381 380
327: 578 577
328: 762 761
329: 896 895
330: 793 792
331: 295 294
332: 488 487
333: 599 598
334: 182 181
335: 25 24
336: 623 622
337: 396 395
338: 898 897
339: 981 980
340: 645 644
341: 806 805
342: 205 204
343: 404 403
344: 234 233
345: 36 35
346: 659 658
347: 285 284
348: 62 61
349: 608 607
350: 632 631
351: 825 824
352: 585 584
353: 685 684
354: 14 13
355: 828 827
356: 720 719
357: 871 870
358: 88 87
359: 716 715
360: 879 878
361: 650 649
362: 464 463
363: 898 897
364: 930 929
365: 194 193
366: 997 996
367: 105 104
368: 776 775
369: 398 397
370: 962 961
371: 434 433
372: 954 953
373: 548 547
374: 989 988
375: 943 942
376: 229 228
377: 866 865
378: 554 553
379: 567 566
380: 379 378
381: 564 563
382: 738 737
383: 468 467
384: 660 659
385: 693 692
386: 784 783
387: 739 738
388: 662 661
389: 474 473
390: 545 544
391: 958 957
392: 703 702
393: 316 315
394: 571 570
395: 95 94
396: 497 496
397: 672 671
398: 676 675
399: 821 820
400: 368 367
401: 7 6
402: 817 816
403: 221 220
404: 839 838
405: 578 577
406: 635 634
407: 453 452
408: 70 69
409: 764 763
410: 78 77
411: 968 967
412: 295 294
413: 483 482
414: 392 391
415: 23 22
416: 389 388
417: 678 677
418: 150 149
419: 863 862
420: 677 676
421: 676 675
422: 455 454
423: 405 404
424: 126 125
425: 753 752
426: 821 820
427: 328 327
428: 773 772
429: 596 595
430: 645 644
431: 829 828
432: 377 376
433: 444 443
434: 813 812
435: 395 394
436: 794 793
437: 641 640
438: 98 97
439: 827 826
440: 824 823
441: 681 680
442: 736 735
443: 288 287
444: 560 559
445: 781 780
446: 556 555
447: 327 326
448: 820 819
449: 859 858
450: 686 685
451: 919 918
452: 267 266
453: 128 127
454: 583 582
455: 446 445
456: 783 782
457: 712 711
458: 378 377
459: 367 366
460: 52 51
461: 316 315
462: 780 779
463: 398 397
464: 435 434
465: 788 787
466: 380 379
467: 235 234
468: 748 747
469: 429 428
470: 91 90
471: 675 674
472: 853 852
473: 674 673
474: 277 276
475: 179 178
476: 264 263
477: 511 510
478: 514 513
479: 979 978
480: 845 844
481: 728 727
482: 904 903
483: 874 873
484: 750 749
485: 659 658
486: 376 375
487: 713 712
488: 393 392
489: 538 537
490: 896 895
491: 879 878
492: 347 346
493: 819 818
494: 210 209
495: 707 706
496: 869 868
497: 319 318
498: 832 831
499: 498 497
500: 71 70
501: 290 289
502: 861 860
503: 295 294
504: 888 887
505: 515 514
506: 222 221
507: 661 660
508: 813 812
509: 969 968
510: 547 546
511: 900 899
512: 58 57
513: 805 804
514: 428 427
515: 453 452
516: 23 22
517: 969 968
518: 718 717
519: 775 774
520: 395 394
521: 521 520
522: 522 521
523: 465 464
524: 317 316
525: 216 215
526: 254 253
527: 696 695
528: 677 676
529: 21 20
530: 318 317
531: 301 300
532: 142 141
533: 877 876
534: 486 485
535: 981 980
536: 516 515
537: 254 253
538: 328 327
539: 385 384
540: 2 1
541: 405 404
542: 387 386
543: 794 793
544: 48 47
545: 641 640
546: 814 813
547: 981 980
548: 354 353
549: 281 280
550: 561 560
551: 683 682
552: 247 246
553: 739 738
554: 370 369
555: 799 798
556: 680 679
557: 915 914
558: 638 637
559: 254 253
560: 705 704
561: 320 319
562: 640 639
563: 487 486
564: 47 46
565: 852 851
566: 749 748
567: 419 418
568: 300 299
569: 507 506
570: 141 140
571: 972 971
572: 895 894
573: 988 987
574: 279 278
575: 268 267
576: 392 391
577: 530 529
578: 679 678
579: 855 854
580: 246 245
581: 645 644
582: 624 623
583: 417 416
584: 203 202
585: 30 29
586: 9 8
587: 585 584
588: 573 572
589: 471 470
590: 504 503
591: 290 289
592: 588 587
593: 230 229
594: 351 350
595: 651 650
596: 615 614
597: 502 501
598: 352 351
599: 472 471
// 600 - 699 omitted to make space to fit answer
700: 247 246
701: 894 893
702: 809 808
703: 382 381
704: 81 80
705: 574 573
706: 507 506
707: 508 507
708: 569 568
709: 947 946
710: 384 383
711: 14 13
712: 627 626
713: 951 950
714: 825 824
715: 657 656
716: 206 205
717: 598 597
718: 300 299
719: 266 265
720: 909 908
721: 206 205
722: 126 125
723: 841 840
724: 586 585
725: 348 347
726: 100 99
727: 361 360
728: 695 694
729: 556 555
730: 66 65
731: 5 4
732: 686 685
733: 488 487
734: 149 148
735: 622 621
736: 476 475
737: 488 487
738: 371 370
739: 331 330
740: 965 964
741: 141 140
742: 396 395
743: 917 916
744: 31 30
745: 924 923
746: 283 282
747: 369 368
748: 519 518
749: 830 829
750: 688 687
751: 374 373
752: 41 40
753: 418 417
754: 766 765
755: 854 853
756: 453 452
757: 521 520
758: 640 639
759: 185 184
760: 41 40
761: 125 124
762: 723 722
763: 341 340
764: 142 141
765: 754 753
766: 459 458
767: 899 898
768: 166 165
769: 374 373
770: 572 571
771: 304 303
772: 352 351
773: 235 234
774: 879 878
775: 736 735
776: 576 575
777: 56 55
778: 102 101
779: 170 169
780: 208 207
781: 135 134
782: 919 918
783: 599 598
784: 37 36
785: 997 996
786: 922 921
787: 502 501
788: 29 28
789: 173 172
790: 54 53
791: 601 600
792: 535 534
793: 64 63
794: 723 722
795: 491 490
796: 685 684
797: 58 57
798: 272 271
799: 261 260
800: 81 80
801: 149 148
802: 129 128
803: 712 711
804: 377 376
805: 151 150
806: 514 513
807: 14 13
808: 838 837
809: 347 346
810: 517 516
811: 442 441
812: 264 263
813: 883 882
814: 447 446
815: 140 139
816: 195 194
817: 841 840
818: 218 217
819: 858 857
820: 28 27
821: 222 221
822: 223 222
823: 906 905
824: 873 872
825: 492 491
826: 826 825
827: 738 737
828: 307 306
829: 185 184
830: 525 524
831: 449 448
832: 646 645
833: 686 685
834: 942 941
835: 433 432
836: 881 880
837: 824 823
838: 641 640
839: 290 289
840: 897 896
841: 4 3
842: 124 123
843: 679 678
844: 524 523
845: 424 423
846: 282 281
847: 625 624
848: 414 413
849: 647 646
850: 129 128
851: 395 394
852: 720 719
853: 318 317
854: 262 261
855: 402 401
856: 413 412
857: 139 138
858: 549 548
859: 472 471
860: 162 161
861: 605 604
862: 67 66
863: 980 979
864: 465 464
865: 912 911
866: 219 218
867: 648 647
868: 619 618
869: 331 330
870: 625 624
871: 360 359
872: 425 424
873: 935 934
874: 89 88
875: 641 640
876: 535 534
877: 404 403
878: 966 965
879: 27 26
880: 281 280
881: 637 636
882: 57 56
883: 152 151
884: 156 155
885: 813 812
886: 340 339
887: 181 180
888: 921 920
889: 306 305
890: 101 100
891: 178 177
892: 417 416
893: 845 844
894: 904 903
895: 295 294
896: 346 345
897: 654 653
898: 357 356
899: 929 928
900: 195 194
901: 499 498
902: 377 376
903: 727 726
904: 570 569
905: 853 852
906: 71 70
907: 580 579
908: 642 641
909: 889 888
910: 559 558
911: 134 133
912: 324 323
913: 120 119
914: 991 990
915: 6 5
916: 708 707
917: 347 346
918: 929 928
919: 454 453
920: 636 635
921: 218 217
922: 739 738
923: 715 714
924: 87 86
925: 782 781
926: 670 669
927: 845 844
928: 79 78
929: 730 729
930: 58 57
931: 216 215
932: 711 710
933: 898 897
934: 871 870
935: 388 387
936: 389 388
937: 944 943
938: 927 926
939: 88 87
940: 617 616
941: 940 939
942: 948 947
943: 927 926
944: 646 645
945: 125 124
946: 615 614
947: 846 845
948: 705 704
949: 998 997
950: 304 303
951: 346 345
952: 675 674
953: 783 782
954: 129 128
955: 69 68
956: 17 16
957: 646 645
958: 559 558
959: 62 61
960: 807 806
961: 571 570
962: 54 53
963: 297 296
964: 771 770
965: 972 971
966: 829 828
967: 786 785
968: 650 649
969: 101 100
970: 705 704
971: 690 689
972: 365 364
973: 304 303
974: 82 81
975: 776 775
976: 495 494
977: 586 585
978: 556 555
979: 77 76
980: 640 639
981: 161 160
982: 910 909
983: 46 45
984: 43 42
985: 162 161
986: 514 513
987: 654 653
988: 668 667
989: 126 125
990: 254 253
991: 133 132
992: 398 397
993: 993 992
994: 357 356
995: 298 297
996: 519 518
997: 904 903
998: 382 381
999: 28 27
1000: 19 18
1001: 939 938
1002: 868 867
1003: 888 887
1004: 576 575
1005: 183 182
1006: 174 173
1007: 679 678
1008: 831 830
1009: 464 463
1010: 876 875
1011: 738 737
1012: 447 446
1013: 385 384
1014: 271 270
1015: 38 37
1016: 28 27
1017: 451 450
1018: 162 161
1019: 847 846
1020: 430 429
1021: 849 848
1022: 207 206
1023: 196 195
1024: 42 41
1025: 709 708
1026: 557 556
1027: 173 172
1028: 788 787
1029: 160 159
1030: 535 534
1031: 555 554
1032: 252 251
1033: 111 110
1034: 476 475
1035: 780 779
1036: 44 43
1037: 190 189
1038: 443 442
1039: 655 654
1040: 7 6
1041: 845 844
1042: 856 855
1043: 274 273
1044: 933 932
1045: 336 335
1046: 185 184
1047: 580 579
1048: 807 806
1049: 286 285
1050: 409 408
1051: 347 346
1052: 461 460
1053: 624 623
1054: 378 377
1055: 903 902
1056: 483 482
1057: 838 837
1058: 809 808
1059: 919 918
1060: 544 543
1061: 458 457
1062: 121 120
1063: 192 191
1064: 126 125
1065: 843 842
1066: 927 926
1067: 390 389
1068: 567 566
1069: 1000 999
Entry 1069 is the first occurrence in this sample set to reach 1,000. I've ran this about a dozen times both in 32bit and 64bit modes and I did not see any value go above 1,000.
I'm not sure but I think that this line in your code is what is giving you your problem(s):
distArray[(int)(random64() % (sampleSize / 2))]++;
I have an image, eg, matrix A;
A= [156 159 158 155 158 156 159 158 157 158;
160 154 157 158 157 159 158 158 158 160;
156 159 158 155 158 156 159 158 157 158;
160 154 157 158 157 159 158 158 158 160;
156 153 155 159 159 155 156 155 155 157;
155 155 155 157 156 159 152 158 156 158;
156 153 157 156 153 155 154 155 157 156;
159 159 156 158 156 159 157 161 162 157;
158 155 158 154 156 160 162 155 159 161;
155 154 157 158 160 160 159 160 158 161]
To get pixel value for RSAT(x,y),
RSAT(x,y) = RSAT(x-1,y-1) + RSAT(x-1,y+1) - RSAT(x-2,y) + I(x-1,y)+ I(x,y); where I is original image(matrixA).
Matrix B (after calculated RSAT):
[0 0 0 0 0 0 0 0 0 0 0;
0 156 159 158 155 158 156 159 158 157 158;
156 475 627 629 629 626 632 631 632 631 475;
475 943 1258 1413 1413 1418 1416 1422 1420 1265 949;
943 1574 2042 2357 2515 2518 2523 2522 2371 2053 1583;
1574 2358 2980 3456 3779 3936 3938 3786 3468 3002 2370;
2358 3291 4080 4712 5193 5514 5513 5192 4730 4096 3317;
3291 4391 5331 6129 6760 7079 7082 6763 6133 5358 4410;
4391 5646 6752 7692 8329 8637 8643 8334 7707 6766 5671;
5646 7069 8321 9266 9881 10205 10208 9906 9283 8341 7084;
7069 8634 9892 10825 11454 11768 11788 11478 10855 9918 8663]
Total sum of Region (bold region) at matrix A = 2041 .
However, sum of Region (bold region ) at matrix B= 1880. As a integral image theory, it suppose return same value as matrix A, 2041.
Here my code (matlab)
Kindly please assist me.
Thank you.
I= [156 159 158 155 158 156 159 158 157 158;
160 154 157 158 157 159 158 158 158 160;
156 159 158 155 158 156 159 158 157 158;
160 154 157 158 157 159 158 158 158 160;
156 153 155 159 159 155 156 155 155 157;
155 155 155 157 156 159 152 158 156 158;
156 153 157 156 153 155 154 155 157 156;
159 159 156 158 156 159 157 161 162 157;
158 155 158 154 156 160 162 155 159 161;
155 154 157 158 160 160 159 160 158 161];
Dummy_Ori_Img =padarray(I,[1 1],'pre') ;
Dummy_Ori_Img2 =padarray(Dummy_Ori_Img,[0 1],'replicate','post') ;
%calculate RSAT
RSAT = zeros(size(Dummy_Ori_Img2));
[Height_Dummy,Width_Dummy]=size (Dummy_Ori_Img2);
for x =1:Height_Dummy
for y = 1:Width_Dummy
if x-2<=0 || (x-2)>Height_Dummy || y>=Width_Dummy ||y==1
RSAT1=0;
else
RSAT1= RSAT(x-2,y);
end
if x-1<=0 || y-1<=0 || (x-1)>Height_Dummy || (y-1)>Width_Dummy
RSAT2=0;
else
RSAT2=RSAT(x-1,y-1);
end
if x-1<=0 || (x-1)>Height_Dummy || (y+1)>Width_Dummy
RSAT3=0;
else
RSAT3=RSAT(x-1,y+1);
end
if x-1<=0 || y<=0 || x>Width_Dummy || y>Height_Dummy
DOI1=0;
else
DOI1=Dummy_Ori_Img(x-1,y);
end
if x<=0 || y<=0 || x>Width_Dummy || y>Height_Dummy
DOI2=0;
else
DOI2=Dummy_Ori_Img(x,y);
end
RSAT(x,y)= RSAT3 + RSAT2-RSAT1 + DOI2 + DOI1;
end
end
RSATnew = RSAT (1:size(Dummy_Ori_Img,1),1: size(Dummy_Ori_Img,2) );
outer_upright_kernel = ones (3,3);
TiltedKernel=ceil(imrotate(outer_upright_kernel,45,'bilinear','loose'));
[Height_tilt,Width_tilt]=size (TiltedKernel);
HalfTilt_x= floor(Width_tilt/2);
HalfTilt_y= floor(Height_tilt/2);
% calculate sum of region
xi=6;
yi=6;
fourpoints = [xi yi HalfTilt_x HalfTilt_y];
row_val=fourpoints(1,1);
col_val=fourpoints(1,2);
img_width=fourpoints(1,3);
img_length=fourpoints(1,4);
if row_val-1<=0 ||col_val-img_width<=0
T1to = 0;
else
T1to = RSATnew(row_val-1,col_val-img_width);
TiltOuter1 = [row_val-1,col_val-img_width];
end
if row_val-1-img_length<=0 || col_val-1<=0
T2to = 0;
else
T2to = RSATnew(row_val-1-img_length,col_val);
TiltOuter2 = [row_val-1-img_length,col_val];
end
if row_val + img_length<=0 ||col_val<=1
T3to = 0;
else
T3to = RSATnew(row_val + img_length,col_val);
TiltOuter3 = [row_val + img_length,col_val];
end
if col_val+img_width+1 <=0
T4to = 0;
else
T4to = RSATnew(row_val,col_val+img_width+1);
TiltOuter4 = [row_val,col_val+img_width+1];
end
TiltOuterSum = T2to + T3to - T1to - T4to;
Based on Lienhart(2002) (http://www.multimedia-computing.de/mediawiki/images/5/52/MRL-TR-May02-revised-Dec02.pdf),
the RSAT (x,y)= RSAT(x-1,y-1) + RSAT(x+1,y-1) - RSAT(x,y-2) + I(x,y) + I(x,y-1)
For your matrix, A
[156 159 158 155 158 156 159 158 157 158;
160 154 157 158 157 159 158 158 158 160;
156 159 158 155 158 156 159 158 157 158;
160 154 157 158 157 159 158 158 158 160;
156 153 155 159 159 155 156 155 155 157;
155 155 155 157 156 159 152 158 156 158;
156 153 157 156 153 155 154 155 157 156;
159 159 156 158 156 159 157 161 162 157;
158 155 158 154 156 160 162 155 159 161;
155 154 157 158 160 160 159 160 158 161].
Then, RSAT of matrix A should be:
[156 159 158 155 158 156 159 158 157 158;
475 627 629 629 626 #632# 631 632 631 475;
787 1258 1413 1413 1418 1416 1422 1420 1265 791;
1099 1886 2357 2515 2518 2523 2522 2371 1895 1108;
1415 2505 #3300# 3779 3936 3938 3786 3310 #2527# 1421;
1717 3137 4237 5037 5514 5513 5034 4255 3147 1734;
2033 3757 5186 6285 6923 6924 6288 5184 3775 2040;
2355 4394 6118 7386 8004 #8012# 7385 6124 4396 2354;
2678 5030 6908 8149 8787 8784 8167 6913 5024 2674;
2988 5501 7376 8621 9245 9262 8633 7382 5508 2992]
Total sum of region (bold region in matrix A - I have altered based on the paper) is 2817. Based on RSAT, should be calculated as 8012 + 632 - 3300 - 2527 = 2817.
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I wrote a simple genetic algorithm that can solve traveling salesman problem with 5 cities. I want to see how it does on a problem with more cities, something like 10, 25, 50, 100, but I can't find a sample date for the problem to try it on. Basically, I am looking for 2D lists or matrices with distances between cities. It would be nice if there is a solution. Where should I look?
Thank You in Advance
A well-known benchmark library for the TSP with instances ranging from as few as 14 to close to 100,000 cities is the TSPLIB. The instances have been solved to optimality, for some instances the optimal solution is also available.
Many of the instances have a real-world background such as travel been cities in Germany, Switzerland, the USA, or in the whole world. Some of the instances represent drilling problems for computer board layout There's also an instance that represents the voyage of Ulysses.
The sources I've found online are quite huge. I might be doing something wrong, but 10 places (cities) take ~0.6s and 11 places take ~7s. The smallest known-solution dataset I could find was 15 places (and considered "small", the "classical" one being 48 places) but perhaps those are for optimized (non-brute force) algorithms. In the end I made my own table with real-world cities:
m
a
a h
s h s u
t a e i g l
r a e t e s
i c r t l e b b a e
c h l a e c o e n o p
h e e r e h n r n h e
t n n d n t n g e e n
maastricht 0 29 20 21 16 31 100 12 4 31 18
aachen 29 0 15 29 28 40 72 21 29 41 12
heerlen 20 15 0 15 14 25 81 9 23 27 13
sittard 21 29 15 0 4 12 92 12 25 13 25
geleen 16 28 14 4 0 16 94 9 20 16 22
echt 31 40 25 12 16 0 95 24 36 3 37
bonn 100 72 81 92 94 95 0 90 101 99 84
hulsberg 12 21 9 12 9 24 90 0 15 25 13
kanne 4 29 23 25 20 36 101 15 0 35 18
ohe 31 41 27 13 16 3 99 25 35 0 38
epen 18 12 13 25 22 37 84 13 18 38 0
Optimal (by program): cities 0-7-4-3-9-5-2-6-1-10-8-0 = 253km
maastricht -> hulsberg -> geleen -> sittard -> ohe -> kanne -> echt
-> heerlen -> bonn -> aachen -> epen -> kanne -> maastricht
The data format readable by the program is a partial table (because it's symmetrical):
29 20 21 16 31 100 12 4 31 18
15 29 28 40 72 21 29 41 12
15 14 25 81 9 23 27 13
4 12 92 12 25 13 25
16 94 9 20 16 22
95 24 36 3 37
90 101 99 84
15 25 13
35 18
38
For me this takes ~6.7 seconds to process on a 3rd gen i7 (i7-3630QM). Program is written in C++, single-threaded and simply brute-forces the possibilities. For testing it might be more practical to remove one place, then it takes ~660ms (0.7s) which is still enough to see if code changes make much of a difference.
For next incomes, i'll paste some more "small" cases:
You can find more tests in here. but the file is ".tsp" extension and you should do a simple parse that translate to the matrix of distances.
(distance in miles)
6 cities, expected: 1248.0
9999 64 378 519 434 200
64 9999 318 455 375 164
378 318 9999 170 265 344
519 455 170 9999 223 428
434 375 265 223 9999 273
200 164 344 428 273 9999
15 cities, expected: 1194.0
-1 141 134 152 173 289 326 329 285 401 388 366 343 305 276
141 -1 152 150 153 312 354 313 249 324 300 272 247 201 176
134 152 -1 24 48 168 210 197 153 280 272 257 237 210 181
152 150 24 -1 24 163 206 182 133 257 248 233 214 187 158
173 153 48 24 -1 160 203 167 114 234 225 210 190 165 137
289 312 168 163 160 -1 43 90 124 250 264 270 264 267 249
326 354 210 206 203 43 -1 108 157 271 290 299 295 303 287
329 313 197 182 167 90 108 -1 70 164 183 195 194 210 201
285 249 153 133 114 124 157 70 -1 141 147 148 140 147 134
401 324 280 257 234 250 271 164 141 -1 36 67 88 134 150
388 300 272 248 225 264 290 183 147 36 -1 33 57 104 124
366 272 257 233 210 270 299 195 148 67 33 -1 26 73 96
343 247 237 214 190 264 295 194 140 88 57 26 -1 48 71
305 201 210 187 165 267 303 210 147 134 104 73 48 -1 30
276 176 181 158 137 249 287 201 134 150 124 96 71 30 -1
Hugeeee 29 cities, expected: 27603
imagem: western sahara
-1 74 4110 3048 2267 974 4190 3302 4758 3044 3095 3986 5093 6407 5904 8436 6963 6694 6576 8009 7399 7267 7425 9639 9230 8320 9300 8103 7799
74 -1 4070 3000 2214 901 4138 3240 4702 2971 3021 3915 5025 6338 5830 8369 6891 6620 6502 7939 7326 7193 7351 9571 9160 8249 9231 8030 7725
4110 4070 -1 1173 1973 3496 892 1816 1417 3674 3778 2997 2877 3905 5057 5442 4991 5151 5316 5596 5728 5811 5857 6675 6466 6061 6523 6165 6164
3048 3000 1173 -1 817 2350 1172 996 1797 2649 2756 2317 2721 3974 4548 5802 4884 4887 4960 5696 5537 5546 5634 7045 6741 6111 6805 6091 5977
2267 2214 1973 817 -1 1533 1924 1189 2498 2209 2312 2325 3089 4401 4558 6342 5175 5072 5075 6094 5755 5712 5828 7573 7222 6471 7289 6374 6187
974 901 3496 2350 1533 -1 3417 2411 3936 2114 2175 3014 4142 5450 4956 7491 5990 5725 5615 7040 6430 6304 6459 8685 8268 7348 8338 7131 6832
4190 4138 892 1172 1924 3417 -1 1233 652 3086 3185 2203 1987 3064 4180 4734 4117 4261 4425 4776 4844 4922 4971 5977 5719 5228 5780 5302 5281
3302 3240 1816 996 1189 2411 1233 -1 1587 1877 1979 1321 1900 3214 3556 5175 4006 3947 3992 4906 4615 4599 4700 6400 6037 5288 6105 5209 5052
4758 4702 1417 1797 2498 3936 652 1587 -1 3286 3374 2178 1576 2491 3884 4088 3601 3818 4029 4180 4356 4469 4497 5331 5084 4645 5143 4761 4787
3044 2971 3674 2649 2209 2114 3086 1877 3286 -1 107 1360 2675 3822 2865 5890 4090 3723 3560 5217 4422 4257 4428 7000 6514 5455 6587 5157 4802
3095 3021 3778 2756 2312 2175 3185 1979 3374 107 -1 1413 2725 3852 2826 5916 4088 3705 3531 5222 4402 4229 4403 7017 6525 5451 6598 5142 4776
3986 3915 2997 2317 2325 3014 2203 1321 2178 1360 1413 -1 1315 2511 2251 4584 2981 2778 2753 4031 3475 3402 3531 5734 5283 4335 5355 4143 3897
5093 5025 2877 2721 3089 4142 1987 1900 1576 2675 2725 1315 -1 1323 2331 3350 2172 2275 2458 3007 2867 2935 2988 4547 4153 3400 4222 3376 3307
6407 6338 3905 3974 4401 5450 3064 3214 2491 3822 3852 2511 1323 -1 2350 2074 1203 1671 2041 1725 1999 2213 2173 3238 2831 2164 2901 2285 2397
5904 5830 5057 4548 4558 4956 4180 3556 3884 2865 2826 2251 2331 2350 -1 3951 1740 1108 772 2880 1702 1450 1650 4779 4197 2931 4270 2470 2010
8436 8369 5442 5802 6342 7491 4734 5175 4088 5890 5916 4584 3350 2074 3951 -1 2222 2898 3325 1276 2652 3019 2838 1244 1089 1643 1130 2252 2774
6963 6891 4991 4884 5175 5990 4117 4006 3601 4090 4088 2981 2172 1203 1740 2222 -1 684 1116 1173 796 1041 974 3064 2505 1368 2578 1208 1201
6694 6620 5151 4887 5072 5725 4261 3947 3818 3723 3705 2778 2275 1671 1108 2898 684 -1 432 1776 706 664 756 3674 3090 1834 3162 1439 1120
6576 6502 5316 4960 5075 5615 4425 3992 4029 3560 3531 2753 2458 2041 772 3325 1116 432 -1 2174 930 699 885 4064 3469 2177 3540 1699 1253
8009 7939 5596 5696 6094 7040 4776 4906 4180 5217 5222 4031 3007 1725 2880 1276 1173 1776 2174 -1 1400 1770 1577 1900 1332 510 1406 1002 1499
7399 7326 5728 5537 5755 6430 4844 4615 4356 4422 4402 3475 2867 1999 1702 2652 796 706 930 1400 -1 371 199 3222 2611 1285 2679 769 440
7267 7193 5811 5546 5712 6304 4922 4599 4469 4257 4229 3402 2935 2213 1450 3019 1041 664 699 1770 371 -1 220 3583 2970 1638 3037 1071 560
7425 7351 5857 5634 5828 6459 4971 4700 4497 4428 4403 3531 2988 2173 1650 2838 974 756 885 1577 199 220 -1 3371 2756 1423 2823 852 375
9639 9571 6675 7045 7573 8685 5977 6400 5331 7000 7017 5734 4547 3238 4779 1244 3064 3674 4064 1900 3222 3583 3371 -1 620 1952 560 2580 3173
9230 9160 6466 6741 7222 8268 5719 6037 5084 6514 6525 5283 4153 2831 4197 1089 2505 3090 3469 1332 2611 2970 2756 620 -1 1334 74 1961 2554
8320 8249 6061 6111 6471 7348 5228 5288 4645 5455 5451 4335 3400 2164 2931 1643 1368 1834 2177 510 1285 1638 1423 1952 1334 -1 1401 648 1231
9300 9231 6523 6805 7289 8338 5780 6105 5143 6587 6598 5355 4222 2901 4270 1130 2578 3162 3540 1406 2679 3037 2823 560 74 1401 -1 2023 2617
8103 8030 6165 6091 6374 7131 5302 5209 4761 5157 5142 4143 3376 2285 2470 2252 1208 1439 1699 1002 769 1071 852 2580 1961 648 2023 -1 594
7799 7725 6164 5977 6187 6832 5281 5052 4787 4802 4776 3897 3307 2397 2010 2774 1201 1120 1253 1499 440 560 375 3173 2554 1231 2617 594 -1