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.
# -*- coding: utf-8 -*-
"""
Created on Sun Jun 14 21:25:06 2020

@author: rishi
"""


n=int(input())
ans=[]
a=list(map(int,input().split()))
oset=set(i for i in range(2*n+1))
aset=set(a)
iset=oset-aset
ilist=sorted(list(iset),reverse=True)
for j in range(n):
    ans.append(ilist[-1])
    de=a.pop(0)
    if(len(a) and a[0]!=de):
        ilist.pop(-1)
        ilist.append(de)
        
        
        #ilist.sort()
    else:
        ilist.pop(-1)

for kk in ans:
    print(kk,end=" ")
    
