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, *X = map(int, open(0).read().split())

x_to_i = {x: i for i, x in enumerate(X, 1)}
I = sorted(range(1, N + 1), key=lambda i: X[i - 1])

T = []
for i in I:
    T += [i] * (i - 1)
for i in I:
    T += [i] * (N - i)
T = iter(T)

C = [0] * (N + 1)
A = []
for x in range(1, N * N + 1):
    if x in x_to_i:
        i = x_to_i[x]
        if C[i] + 1 != i:
            print("No")
            quit()
    else:
        i = next(T)
    C[i] += 1
    A.append(i)

print("Yes")
print(*A)