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 math as ma
# import sys
# input=sys.stdin.readline

n=int(input())
a=list(map(int,input().split()))
e=0
for i in range(n):
    if a[i]-i-1>0:
        e=1
        print(-1)
        break
if e==0:
    b=[-1]*n
    for i in range(n-1):
        if a[i]!=a[i+1]:
            b[i+1]=a[i]
    c=set(a)
    d=[]
    for i in range(2*(10**5)):
        if i not in c:
            d.append(i)
    j=0
    for i in range(n):
        if b[i]==-1:
            b[i]=d[j]
            j+=1
    print(*b)