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:
def main():
    n = int(raw_input())
    b = map(int, raw_input().split())
    m = n * n
    a = [0] * m
    for i, x in enumerate(b):
        a[x-1] = i + 1
    j = 0
    for i in xrange(m):
        if a[i] > 0:
            x = a[i]
            for k in xrange(x - 1):
                while a[j] != 0:
                    if j >= i:
                        print "No"
                        return
                    j += 1
                a[j] = -x
    j = m - 1
    for i in xrange(m - 1, -1, -1):
        if a[i] > 0:
            x = a[i]
            for k in xrange(n - x):
                while a[j] != 0:
                    if j <= i:
                        print "No"
                        quit()
                        return
                    j -= 1
                a[j] = -x
    print "Yes"
    for x in a:
        print x if x > 0 else -x,
    print
main()