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
import math
 
n = int(sys.stdin.readline().strip())
l = list(map(int, sys.stdin.readline().strip().split(' ')))

possible = True
for i,li in enumerate(l):
	if li > i+1:
		possible = False

if not possible:
	print(-1)
else:
	inf = 10**6
	res = [inf for i in range(n)]

	taken = set(res)

	for i in range(n-1):
		if l[i] != l[i+1]:
			res[i+1] = l[i]

	curr = 0
	while curr in taken:
		curr += 1
	for i in range(n):
		if res[i] == inf:
			res[i] = curr
			curr += 1
			while curr in taken:
				curr += 1

	print(' '.join([str(x) for x in res]))

