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.
n = int(input())


arr = list(map(int, input().split(' ')))
_max = max(arr)
count = dict()
seq = []
for i in range(n):
    if arr[i] not in count:
        count[arr[i]] = 1
    else:
        count[arr[i]] = count[arr[i]] + 1 
if arr[0] > 1:
    print(-1)
else:
    error = 0
    if arr[0] == 0:
        next_zero = 1
        while (next_zero in count) and (count[next_zero] > 0):
            next_zero += 1
        seq.append(next_zero)
        count[next_zero] = 1
        while (next_zero in count) and (count[next_zero] > 0):
            next_zero += 1
    if arr[0] == 1:
        seq.append(0)
        count[0] = 1
        next_zero = 1
    for i in range(1, n):
        if arr[i] > i + 1:
            error = 1
            break
        else:
            count[arr[i - 1]] = count[arr[i - 1]] - 1
            if count[arr[i - 1]] == 0:
                seq.append(arr[i - 1])
                count[arr[i - 1]] = 1
            else:
                while (next_zero in count) and (count[next_zero] > 0):
                    next_zero += 1
                seq.append(next_zero)
                if next_zero <= _max:
                    count[next_zero] = 1
                else:
                    count[next_zero] = 0
    if error == 1:
        print(-1)
    else:
        print(*seq)
