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 PYTHON3):

Solution:
N = int(input())
ans = [-1] * (N ** 2)
X = [int(x)-1 for x in input().split()]
for i, x in enumerate(X):
    ans[x] = i+1
left, right = [], []
for i in range(N):
    l_cnt, r_cnt = i, N - (i+1)
    left.extend([(X[i], i+1)] * l_cnt)
    right.extend([(X[i], i+1)] * r_cnt)
l, r = 0, N ** 2 - 1
left.sort()
right.sort()
for _, x in left:
    while ans[l] != -1:
        l += 1
    ans[l] = x
for _, x in reversed(right):
    while ans[r] != -1:
        r -= 1
    ans[r] = x
counter = [[] for _ in range(N)]
for i, a in enumerate(ans):
    counter[a-1].append(i)
if all(counter[i].index(x) == i for i, x in zip(range(N), X)):
    print("Yes")
    print(*ans)
else:
    print("No")
assert(all(a != -1 for a in ans))
assert(all(len(row) == N for row in counter))