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symmetricgrid Batch , stdin/stdout

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symmetricgrid.html

Symmetric Grid

Problem Statement

There is an H × W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string Si.

Snuke can apply the following operation to this grid any number of times:

  • Choose two different rows and swap them. Or, choose two different columns and swap them.

Snuke wants this grid to be symmetric. That is, for any 1 ≤ i ≤ H and 1 ≤ j ≤ W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.

Determine if Snuke can achieve this objective.

Constraints

  • 1 ≤ H ≤ 12
  • 1 ≤ W ≤ 12
  • |Si| = W
  • Si consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

H W
S1
S2
:
SH

Output

If Snuke can make the grid symmetric, print YES; if he cannot, print NO.

Sample Input 1

2 3
arc
rac

Sample Output 1

YES

If the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:

Sample Input 2

3 7
atcoder
regular
contest

Sample Output 2

NO

Sample Input 3

12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv

Sample Output 3

YES

sampleimg.png

Tags

AtCoder

Subtasks and Limits

Subtask Score #TC Time Memory Scoring
1100571s256MBMinimum
2031s256MBMinimum

Judge Compile Command

g++-8 ans.cpp -o symmetricgrid -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512

Accepted Submissions

subIDUserTimeMax Time

Past Submissions

subIDUserTimeScore
mrJudge 09.05.20
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