Problem: For given a sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$, print the previous permutation and the next permutation in lexicographic order.

Constraints

* $1 \leq n \leq 9$
* $a_i$ consist of $1, 2, ..., n$

Input

A sequence is given in the following format.


$n$
$a_0 \; a_1 \; ... \; a_{n-1}$


Output

Print the previous permutation, the given sequence and the next permutation in the 1st, 2nd and 3rd lines respectively. Separate adjacency elements by a space character. Note that if there is no permutation, print nothing in the corresponding line.

Examples

Input

3
2 1 3


Output

1 3 2
2 1 3
2 3 1


Input

3
3 2 1


Output

3 1 2
3 2 1

Solution (in PYTHON3):

Solution:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# FileName: 	permutation
# CreatedDate:  2020-07-08 19:01:42 +0900
# LastModified: 2020-07-08 19:17:50 +0900
#


import os
import sys
# import numpy as np
# import pandas as pd
from itertools import permutations as nPr
from copy import deepcopy


def main():
    n = int(input())
    a = list(map(int, input().split()))
    s = sorted(deepcopy(a))
    p = list(nPr(s))
    inde = p.index(tuple(a))
#    print(p)
#    print(inde)
    if inde!=0:
        print(p[inde-1][0], end="")
        for i in range(1, n):
            print(" {}".format(p[inde-1][i]), end="")
        print()
    print(p[inde][0], end="")
    for i in range(1, n):
        print(" {}".format(p[inde][i]), end="")
    print()
    if inde!=len(p)-1:
        print(p[inde+1][0], end="")
        for i in range(1, n):
            print(" {}".format(p[inde+1][i]), end="")
        print()
    


if __name__ == "__main__":
    main()