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 deque
N = int(input())
List = [int(x) for x in input().split()]
for i in range(N):
    if(List[i]>i+1):
        print(-1)
        exit()
Nahi = list(set(list(range(N+1))).difference(set(List)))
Nahi.sort()
Ans = [Nahi[0]]
Added = deque()
Added.append(List[0])
index = 1
for i in range(1,N):
    if(List[i]==List[i-1]):
        if(Added[-1]!=List[i]):
            Added.append(List[i])
        Ans.append(Nahi[index])
        index+=1
    else:
        Ans.append(Added[0])
        Added.popleft()
        Added.append(List[i])
print(*Ans)
    
