Problem:
Score : 400 points

Problem Statement

Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:

N
b_1 \dots b_N

Output

If there is no sequence of N operations after which a would be equal to b, print -1.
If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in Python (3.8.2) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
import sys
from collections import deque, defaultdict
from math import sqrt, factorial, gcd, ceil
# def input(): return sys.stdin.readline()[:-1] # warning not \n
# def input(): return sys.stdin.buffer.readline().strip() # warning bytes
# def input(): return sys.stdin.buffer.readline().decode('utf-8')
import string
# string.ascii_lowercase
from bisect import bisect_left

def solve():
    n = int(input())
    ans = [0] * n
    a = [int(x) for x in input().split()]
    ok = 1
    cur = n - 1
    while ok and a:
        ok = 0
        i = len(a) - 1
        while i >= 0:
            if a[i] - 1 == i:
                ok = a[i]
                a.pop(i)
                break
            i -= 1
        ans[cur] = ok
        cur -= 1

    if a:
        print(-1)
    else:
        for e in ans:
            print(e)
t = 1
# t = int(input())
for case in range(1,t+1):
    ans = solve()


"""

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"""