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 collections import Counter, defaultdict, deque
import bisect
from sys import stdin, stdout
from itertools import repeat
import math

# sys.stdin = open('input')

def inp(force_list=False):
    re = map(int, raw_input().split())
    if len(re) == 1 and not force_list:
        return re[0]
    return re

def inst():
    return raw_input().strip()

def gcd(x, y):
   while(y):
       x, y = y, x % y
   return x


def my_main():
    t = 1
    for _ in range(t):
        n = inp()
        da = inp(True)
        last = 0
        ct = 0
        st = set(i for i in range(max(da)))
        ans = [-1] * n
        last = 0
        for i in range(n):
            if da[i] != last:
                ans[i] = last
                st.discard(last)
            last = da[i]
        st.discard(last)
        li = sorted(list(st))
        idx = 0
        for i in range(n):
            if ans[i]==-1:
                if idx<len(li):
                    ans[i] = li[idx]
                    idx += 1
                else:
                    if i==0:
                        ans[i] = da[i]^1
                    else:
                        ans[i] = ans[i-1]
            else:
                if idx<len(li) and ans[i] > li[idx]:
                    print -1
                    return
        if idx != len(li):
            print -1
            return
        print ' '.join(map(str, ans))







my_main()
