Vertical Permutation

J: Horizontal-Vertical Permutation

Problem Statement

You are given a positive integer N. Your task is to determine if there exists a square matrix A whose dimension is N that satisfies the following conditions and provide an example of such matrices if it exists. A_{i, j} denotes the element of matrix A at the i-th row and j-th column.

• For all i, j (1 \leq i, j \leq N), A_{i, j} is an integer that satisfies 1 \leq A_{i, j} \leq 2N - 1.
• For all k = 1, 2, ..., N, a set consists of 2N - 1 elements from the k-th row or k-th column is \{1, 2, ..., 2N - 1\}.

If there are more than one possible matrices, output any of them.

Input

N

Input consists of one line, which contains the integer N that is the size of a square matrix to construct.

Constraint

• N is an integer that satisfies 1 \leq N \leq 500.

Output

Output No in a single line if such a square matrix does not exist.

If such a square matrix A exists, output Yes on the first line and A after that. More specifically, follow the following format.

Yes A_{1, 1} A_{1, 2} ... A_{1, N} A_{2, 1} A_{2, 2} ... A_{2, N} : A_{N, 1} A_{N, 2} ... A_{N, N}

Sample Input 1

4

Output for Sample Input 1

Yes 2 6 3 7 4 5 2 1 1 7 5 6 5 3 4 2

Sample Input 2

3

Output for Sample Input 2

No

Example

Input

4

Output

Yes 2 6 3 7 4 5 2 1 1 7 5 6 5 3 4 2

inputFormat

outputFormat

output any of them.

Input

N

Input consists of one line, which contains the integer N that is the size of a square matrix to construct.

Constraint

• N is an integer that satisfies 1 \leq N \leq 500.

Output

Output No in a single line if such a square matrix does not exist.

If such a square matrix A exists, output Yes on the first line and A after that. More specifically, follow the following format.

Yes A_{1, 1} A_{1, 2} ... A_{1, N} A_{2, 1} A_{2, 2} ... A_{2, N} : A_{N, 1} A_{N, 2} ... A_{N, N}

Sample Input 1

4

Output for Sample Input 1

Yes 2 6 3 7 4 5 2 1 1 7 5 6 5 3 4 2

Sample Input 2

3

Output for Sample Input 2

No

Example

Input

4

Output

Yes 2 6 3 7 4 5 2 1 1 7 5 6 5 3 4 2

样例

4

Yes
2 6 3 7
4 5 2 1
1 7 5 6
5 3 4 2

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