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())
X = list(map(lambda x: int(x)-1, input().split()))
Ans = [0] * (N*N)
for i, x in enumerate(X, 1):
    Ans[x] = i
Y = list(range(1, N+1))
Y.sort(key=lambda y: X[y-1])
q1 = []
q1_cnt = [0] * (N+1)
for y in Y:
    q1 += [y] * (y-1)
    q1_cnt[y] += y-1
q1.reverse()
q2 = []
for i, a in enumerate(Ans[:]):
    if a==0:
        if q1:
            v = q1.pop()
            Ans[i] = v
            q1_cnt[v] -= 1
        elif q2:
            Ans[i] = q2.pop()
        else:
            print("No")
            exit()
    else:
        if q1_cnt[a] > 0:
            print("No")
            exit()
        q2 += [a] * (N-a)
print("Yes")
print(" ".join(map(str, Ans)))