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
readline = sys.stdin.readline
from collections import deque

def solve():
    N = int(readline())
    A = list(map(int, readline().split()))

    nonused = set(range(N+1)) - set(A)
    q = deque(sorted(nonused))

    m = 0

    ans = [0] * N
    for i in range(N):
        if A[i] == m:
            ans[i] = q.popleft()
        else:
            ans[i] = m
            if q and q[0] == m:
                q.popleft()
            m = A[i]

    print(*ans)

solve()