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.
"""do not use with graph questions"""
from sys import stdin
from collections import Counter
n = int(stdin.readline())
arr = list(map(int,stdin.readline().split()))
cou = Counter()
fl = 0
for val in arr:
    cou[val] += 1
#if arr[0]==0:
    #for ind,val in enumerate(arr):
        #if val>ind:
see = set(arr)
if not fl:
    i = 1
    add = -1
    if arr[0]==1:
        fin=[0]
        cou[1]-=1
        if cou[1] == 0:
            add = 1
    else:
        fin = []
        for x in range(1,10**6):
            if x not in see:
                fin.append(x)
                break
        cou[0] -= 1
        if cou[0] == 0:
            add = 0
    se = set(fin)
    a = arr[0]+1
    while len(fin) != n:
        #print(i,fin,se)
        if add != -1:
            fin.append(add)
            se.add(add)
            add = -1
            cou[arr[i]]-=1
            if cou[arr[i]]==0:
                add = arr[i]
            i += 1
            continue
        while cou.get(a) or a in se:
            a += 1
        fin.append(a)
        se.add(a)
        cou[arr[i]]-=1
        if cou[arr[i]]==0:
            add = arr[i]
        i += 1
    for i in fin:
        print(i,end=' ')