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 collections as cc
import bisect as bi
input=sys.stdin.readline
I=lambda:list(map(int,input().split()))
n,=I()
l=I()
ans=[-1]*n
temp=[]
visi=[0]*(n+1)
visi[l[-1]]=1
for i in range(n-1,0,-1):
	if l[i]!=l[i-1]:
		ans[i]=l[i-1]
		visi[l[i-1]]=1
j=0
for i in range(n):
	if ans[i]==-1:
		while visi[j]==1:
			j+=1
		ans[i]=j
		j+=1
print(*ans)