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 itertools
def brute(arr):
    arrMax = max(arr)
    productArrs = []
    for i in arr:
        productArrs.append(list(range(arrMax)))
    for barr in itertools.product(*productArrs):
        # print(barr)
        works = True
        for i in range(len(arr)):
            # if barr == (1, 1, 1, 0):
            #     print(i, set(barr[i:i+1]), set(range(arr[i])))
            currSet = set(barr[:i+1])
            for elem in range(arr[i]):
                if elem not in currSet:
                    works = False
                    break
            if arr[i] == barr[i]:
                works = False
            if not works:
                break
            # if not set(barr[:i+1]) == set(range(arr[i])):
            #     works = False
            #     break
        if works:
            return barr
    return []

def test():
    # arr = [1, 2, 3]
    # arr = [0, 0, 0, 2]
    for arr in [
        [1,2,3],
        [0,0,0,2],
        [1,1,3],
    ]:
        b = brute(arr)
        print(b)

def main():
    n = int(input())
    arr = [int(x) for x in input().split()]
    result = brute(arr)
    if len(result) == 0:
        print('-1')
    else:
        print(' '.join(str(x) for x in result))

main()
# test()