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.
production = True

import sys, math

def input(input_format = 0, multi = 0):

    if multi > 0: return [input(input_format) for i in range(multi)]
    else:
        next_line = sys.stdin.readline()

        if input_format >= 10:
            use_list = False
            input_format = int(str(input_format)[-1])
        else: use_list = True

        if input_format == 0: formatted_input = [next_line]
        elif input_format == 1: formatted_input = list(map(int, next_line.split()))
        elif input_format == 2: formatted_input = list(map(float, next_line.split()))
        elif input_format == 3: formatted_input = next_line.split()
        elif input_format == 4: formatted_input = (lambda x: [x[0], list(map(int, x[1:]))])(next_line.split())
        elif input_format == 5: formatted_input = (lambda x: [x[0], list(map(float, x[1:]))])(next_line.split())
        else: formatted_input = [next_line]

        return formatted_input if use_list else formatted_input[0]


def out(output_line, output_format = 0, newline = True):

    formatted_output = ""

    if output_format == 0: formatted_output = str(output_line)
    elif output_format == 1: formatted_output = " ".join(map(str, output_line))
    elif output_format == 1: formatted_output = "\n".join(map(str, output_line))

    print(formatted_output, end = "\n" if newline else "")


def log(*args):
    if not production:
        print("$$$")
        print(*args)


#
#   >>>>>>>>>>>>>>> START OF SOLUTION <<<<<<<<<<<<<<
#


def solve():

    n = input(11)
    a = input(1)

    if a != sorted(a):
        out(-1)
        return

    y = set(a)
    p = []

    for i in range(3 * (10 ** 6), -1, -1):
        if i not in y:
            p.append(i)

    k = []

    log(a)

    for i, j in enumerate(a):
        log(i, j)
        k.append(p.pop())

        if i < n - 1 and j < a[i + 1]:
            p.append(j)

    log(k)
    out(k, 1)

    return


# for i in range(input(11)): solve()
solve()

#
#   >>>>>>>>>>>>>>>> END OF SOLUTION <<<<<<<<<<<<<<<
#
