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.

def solve_test_case(t):
    n = int(input())
    a = parse_array(int)
    a_set = set(a)
    b = []
    b_set = set()
    mex = 0
    max_b = -1

    def add_to_b(v):
        nonlocal b
        nonlocal b_set
        nonlocal mex
        nonlocal max_b
        b.append(v)
        b_set.add(v)
        max_b = max(max_b, v)
        if v == mex:
            while mex in b_set:
                mex += 1

    if a[0] == 1:
        add_to_b(0)
    elif a[0] > 1:
        print(-1)
        return
    else:
        i = 1
        while True:
            if i not in a_set:
                add_to_b(i)
                break
            i += 1

    possible = True
    for i in range(1, n):
        if a[i] > a[i-1]:
            add_to_b(a[i-1])
            if mex != a[i]:
                possible = False
                break
        else:
            v = max_b + 1
            while True:
                if v not in a_set:
                    add_to_b(v)
                    break
                v+= 1

    if possible:
        print(" ".join(list(map(str, b))))
    else:
        print(-1)


def parse_array(f):
    return list(map(f, input().split()))

# def solve():
#     T = int(input())

#     for t in range(T):
#         solve_test_case(t)

if __name__ == "__main__":
    solve_test_case(0)
