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.
import sys
input = sys.stdin.buffer.readline
def prog():
    n = int(input())
    array = list(map(int,input().split()))
    output = [-1]*n
    to_place = []
    prev = -1
    for i in range(n):
        curr = array[i]
        if curr != prev:
            output[i] = prev
            to_place.extend(list(range(prev+1,curr))[::-1])
            prev = curr
    idx = 0
    for i in range(n):
        if output[i] == -1:
            if idx >= len(to_place):
                output[i] = 10**6
            else:
                output[i] = to_place[idx]
                idx += 1
    sys.stdout.write(" ".join(map(str,output)) + '\n')
prog()
            
