Problem: 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

Solution (in PYTHON):

Solution:
import itertools as ite
import math
import random

INF = 10 ** 18
MOD = 10 ** 9 + 7

N = input()
x = map(int, raw_input().split())

ls = []
for i in range(N):
    ls += [(x[i] - 1, i + 1)]
ls.sort()
ans = [-1] * (N * N)

pos = 0
for id, num in ls:
    ans[id] = num
    cnt = num - 1
    while cnt > 0:
        if pos >= id:
            print "No"
            exit()
        if ans[pos] == -1:
            ans[pos] = num
            cnt -= 1
        pos += 1

pos = N * N - 1

for id, num in ls[::-1]:
    cnt = N - num
    while cnt > 0:
        if pos <= id:
            print "No"
            exit()
        if ans[pos] == -1:
            ans[pos] = num
            cnt -= 1
        pos -= 1

print "Yes"
print " ".join(map(str, ans))