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.
#!/usr/bin/env pypy
from __future__ import division, print_function

import os
import sys
from __builtin__ import xrange as range
from cStringIO import StringIO
from future_builtins import ascii, filter, hex, map, oct, zip
from io import IOBase

import __pypy__


def main():
    n = int(input())
    a = [int(ai) for ai in input().split()]

    x, b = 0, []
    dup_idx = []
    for i in range(n):
        if a[i] == x:
            b.append(x + 1)
            dup_idx.append(len(b) - 1)
        else:
            for j in reversed(range(x + 1, a[i])):
                if dup_idx:
                    b[dup_idx.pop()] = j
                else:
                    print(-1)
                    return
            b.append(x)
            x = a[i]

    # ftree = FenwickTree([0] * (n + 1))
    # seen = set()
    # for i in range(n):
    #     if b[i] not in seen:
    #         seen.add(b[i])
    #         ftree.update(b[i], 1)
    #     lo, hi = 0, n + 1
    #     while lo < hi:
    #         mi = (lo + hi) // 2
    #         if ftree.query(mi) < mi:
    #             hi = mi
    #         else:
    #             lo = mi + 1
    #     if a[i] != lo - 1:
    #         print(-1)
    #         return

    print(*b)


class FenwickTree:
    def __init__(self, x):
        """transform list into BIT"""
        self.bit = x
        for i in range(len(x)):
            j = i | (i + 1)
            if j < len(x):
                x[j] += x[i]

    def update(self, idx, x):
        """updates bit[idx] += x"""
        while idx < len(self.bit):
            self.bit[idx] += x
            idx |= idx + 1

    def query(self, end):
        """calc sum(bit[:end])"""
        x = 0
        while end:
            x += self.bit[end - 1]
            end &= end - 1
        return x

    def findkth(self, k):
        """Find largest idx such that sum(bit[:idx]) <= k"""
        idx = -1
        for d in reversed(range(len(self.bit).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(self.bit) and k >= self.bit[right_idx]:
                idx = right_idx
                k -= self.bit[idx]
        return idx + 1


# region fastio

BUFSIZE = 8192


class FastI(IOBase):
    def __init__(self, file):
        self._fd = file.fileno()
        self._buffer = StringIO()
        self.newlines = 0

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count("\n") + (not b)
            ptr = self._buffer.tell()
            self._buffer.seek(0,
                              2), self._buffer.write(b), self._buffer.seek(ptr)
        self.newlines -= 1
        return self._buffer.readline()


class FastO(IOBase):
    def __init__(self, file):
        self._fd = file.fileno()
        self._buffer = __pypy__.builders.StringBuilder()
        self.write = lambda s: self._buffer.append(s)

    def flush(self):
        os.write(self._fd, self._buffer.build())
        self._buffer = __pypy__.builders.StringBuilder()


def print(*args, **kwargs):
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


sys.stdin, sys.stdout = FastI(sys.stdin), FastO(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion

if __name__ == "__main__":
    main()
