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.


def main():
    n = int(input())
    ar = list(map(int, input().split()))
    if n == 1:
        print((1, 0)[ar[0]>0])
        return
    res = [-1] * n
    s = set(ar)
    mx = -1
    for i in range(1, n):
        if ar[i] > ar[i-1]:
            res[i] = ar[i-1]
            mx = max(mx, res[i])
    j = 0
    for i in range(n):
        if res[i] == -1:
            while j in s:
                j += 1
            res[i] = j
            mx = max(mx, j)
            j += 1
    if ar[n-1] - mx > 1:
        print(-1)
        return
    for x in res:
        print(x, end = ' ')
    print()

main()