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.
from sys import stdin, stdout
import heapq as hq
from collections import defaultdict

t = 1
for tc in range(t):
    n = int(stdin.readline())
    ar = list(map(int, stdin.readline().split()))
    resar=[-1 for _ in range(n)]
    res=1

    if ar[0]>1:
        res=-1
    else:
        if ar[0]==1:
            resar[0]=0
            lastval=1
            curmex=1
            curnext=1
            nextskipi=0
        else:  #ar[0]==0
            i=1
            while i<n and ar[i]<=ar[i-1]+1:
                i+=1
            resar[0] = ar[i-1]+1
            lastval = 0
            curmex = 0
            curnext = resar[0]+1
            nextskipi = 0

        while nextskipi<n-1 and ar[nextskipi] < curnext:
            nextskipi += 1
        while ar[nextskipi]==curnext:
            curnext+=1
            while nextskipi<n-1 and ar[nextskipi]<curnext:
                nextskipi+=1
        sofar=set()
        sofar.add(resar[0])

        for i in range(1,n):
            if ar[i]==lastval:
                resar[i]=curnext
                sofar.add(curnext)
                curnext+=1
                while nextskipi<n-1 and ar[nextskipi] < curnext:
                    nextskipi += 1
                while ar[nextskipi] == curnext:
                    curnext += 1
                    while nextskipi<n-1 and ar[nextskipi] < curnext:
                        nextskipi += 1
            else:
                resar[i] = curmex
                sofar.add(curmex)
                while curmex in sofar:
                    curmex+=1
                if curmex!=ar[i]:
                    res=-1
                    break

    if res==-1:
        stdout.write(str(res) + "\n")
    else:
        for val in resar:
            stdout.write(str(val) + " ")
        stdout.write("\n")
