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北京大学《ACM-ICPC竞赛训练》暑期课面向全球招生。容量有限,报名从速!
Language:
Rotating Rings
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 2021Accepted: 786

Description

11111
12221
12321
12221
11111
Figure (a)
1234
5678
9101112
13141516
Figure (b)
9512
137113
146104
1516128
Figure (c)
Any square grid can be viewed as one or more rings, one inside the other. For example, as shown in figure (a), a 5 * 5 grid is made of three rings, numbered 1,2 and 3 (from outside to inside.) A square grid of size N is said to be sorted, if it includes the values from 1 to N2 in a row-major order, as shown in figure (b) for N = 4. We would like to determine if a given square grid can be sorted by only rotating its rings. For example, the grid in figure (c) can be sorted by rotating the first ring two places counter-clockwise, and rotating the second ring one place in the clockwise direction.

Input

Your program will be tested on one or more test cases. The first input line of a test case is an integer N which is the size of the grid. N input lines will follow, each line made of N integer values specifying the values in the grid in a row-major order. Note than 0 < N ≤ 1,000 and grid values are natural numbers less than or equal to 1,000,000.

The end of the test cases is identified with a dummy test case with N = 0.

Output

For each test case, output the result on a single line using the following format:

k. result

Where k is the test case number (starting at 1), and result is "YES" or "NO" (without the double quotes.)

Sample Input

4
9 5 1 2
13 7 11 3
14 6 10 4
15 16 12 8
3
1 2 3
5 6 7
8 9 4
0

Sample Output

1. YES
2. NO

Source

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