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
range = xrange
input = raw_input

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

empty = []

big = 10**6 + 10
B = []
i = 0
counter = [0] * big
for j in range(n):
    a = A[j]
    B.append(-1)
    empty.append(j)
    
    while True:
        while counter[i]:
            i += 1
        if i == a:
            break
        if empty:
            k = empty.pop()
            B[k] = i
            counter[i] += 1
        else:
            print -1
            sys.exit()

for j in empty:
    B[j] = 10**6

print ' '.join(str(x) for x in B)
