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 queue import Queue


def main():
    test = 1
    for _ in range(test):
        n = int(input())
        ara = [int(num) for num in input().split()]
        mark = [True for _ in range(n + 1)]
        for num in ara:
            mark[num] = False

        take_from = Queue()
        for index in range(n + 1):
            if mark[index]:
                take_from.put(index)
        
        ans = []
        ans.append(take_from.get())
        for index in range(1, n):
            if ara[index] != ara[index - 1]:
                ans.append(ara[index - 1])
            elif not take_from.empty():
                ans.append(take_from.get())
            else:
                ans.append(n + 1)
        
        ans = ' '.join(map(str, ans))
        print(ans)


if __name__ == "__main__":
    main()
