atcoder#AGC008D. [AGC008D] K-th K

[AGC008D] K-th K

Score : 800800 points

Problem Statement

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

  • aa is N2N^2 in length, containing NN copies of each of the integers 11, 22, ......, NN.
  • For each 1iN1 \leq i \leq N, the ii-th occurrence of the integer ii from the left in aa is the xix_i-th element of aa from the left.

Constraints

  • 1N5001 \leq N \leq 500
  • 1xiN21 \leq x_i \leq N^2
  • All xix_i are distinct.

Input

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

NN

x1x_1 x2x_2 ...... xNx_N

Output

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

3
1 5 9
Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer 22 from the left in aa in the output is the fifth element of aa from the left. Similarly, the condition is satisfied for the integers 11 and 33.

2
4 1
No