Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.
from collections import deque
import sys

N = int(input())

A = [int(_) for _ in input().split()]

jokers = deque()

B = [-1] * N
current = 0


for i, el in enumerate(A):
    jokers.append(i)
    if el != current:
        for j in range(el - current):
            if not jokers:
                print(-1)
                sys.exit(0)
            p = jokers.pop()
            if A[p] == current + j:
                print(-1)
                sys.exit(0)
            else:
                B[p] = current + j
        current = el

while jokers:
    current += 1
    p = jokers.pop()
    B[p] = current

print(' '.join(map(str, B)))
