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())
a = list(map(int, input().split()))

ans = [-1] * (n ** 2)
for i in range(n):
    ans[a[i] - 1] = i + 1


b = sorted([(a[i], i + 1) for i in range(n)], reverse=True)
stack = []
for _, val in b:
    for _ in range(val - 1):
        stack.append(val)

for i in range(n ** 2):
    if ans[i] == -1:
        if not stack:
            continue
        ans[i] = stack.pop()


b = sorted([(a[i], i + 1) for i in range(n)])
stack = []
for _, val in b:
    for _ in range(n - val):
        stack.append(val)

for i in range(n ** 2)[::-1]:
    if ans[i] == -1:
        if not stack:
            continue
        ans[i] = stack.pop()


cnt = [0] * (n + 1)
for i in range(n ** 2):
    cnt[ans[i]] += 1
    if cnt[ans[i]] == ans[i]:
        if a[ans[i] - 1] == i + 1:
            continue
        else:
            print("No")
            exit()     
print("Yes")
print(*ans)