K-th K

You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.

• a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
• For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.

Constraints

• 1 ≤ N ≤ 500
• 1 ≤ x_i ≤ N^2
• All x_i are distinct.

Input

The input is given from Standard Input in the following format:

N x_1 x_2 ... x_N

Output

If there does not exist an integer sequence a that satisfies all the conditions, print No. If there does exist such an sequence a, print Yes in the first line, then print an instance of a in the second line, with spaces inbetween.

Examples

Input

3 1 5 9

Output

Yes 1 1 1 2 2 2 3 3 3

Input

2 4 1

Output

No

inputFormat

Input

The input is given from Standard Input in the following format:

N x_1 x_2 ... x_N

outputFormat

Output

If there does not exist an integer sequence a that satisfies all the conditions, print No. If there does exist such an sequence a, print Yes in the first line, then print an instance of a in the second line, with spaces inbetween.

Examples

Input

3 1 5 9

Output

Yes 1 1 1 2 2 2 3 3 3

Input

2 4 1

Output

No

样例

2
4 1

No