Permutation

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

inputFormat

Input

A sequence is given in the following format.

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

outputFormat

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

样例

3
3 2 1

3 1 2
3 2 1

</p>