Problem Statement

You are given $a permutation P = (P_1, \dots, P_N)$ of $(1, \dots, N)$, where $(P_1, \dots, P_N) \neq (1, \dots, N)$.
Assume that P is the K-th lexicographically smallest among all permutations of $(1 \dots, N).$ Find the (K-1)-th lexicographically smallest permutation.
What are permutations?

A permutation of $(1, \dots, N)$ is an arrangement of $(1, \dots, N) into a$ sequence.

What is lexicographical order?

For sequences of length $N, A = (A_1, \dots, A_N)$ and $B = (B_1, \dots, B_N), A$ is said to be strictly lexicographically smaller than B if and only if there is an integer $1 \leq i \leq N$ that satisfies both of the following.

• $(A_{1},\ldots,A_{i-1}) = (B_1,\ldots,B_{i-1})$.
• A_i < B_i.

Input

The input is given from Standard Input in the following format:
N
$P_1 \ldots P_N$

Output

Let $Q = (Q_1, \dots, Q_N)$ be the sought permutation. Print $Q_1, \dots, Q_N$ in a single line in this order, separated by spaces.

Constraints

• $2 \leq N \leq 100$
• $1 \leq P_i \leq N$ $, (1 \leq i \leq N)$
• $P_i \neq P_j$ $, (i \neq j)$
• $(P_1, \dots, P_N) \neq (1, \dots, N)$
• All values in the input are integers.

Sample Input 1

3
3 1 2

Sample Output 1

2 3 1

Here are the permutations of (1, 2, 3) in ascending lexicographical order.

• (1, 2, 3)
• (1, 3, 2)
• (2, 1, 3)
• (2, 3, 1)
• (3, 1, 2)
• (3, 2, 1)

Therefore, P = (3, 1, 2) is the fifth smallest, so the sought permutation, which is the fourth smallest (5 - 1 = 4), is (2, 3, 1).

Sample Input 2

10
9 8 6 5 10 3 1 2 4 7

Sample Output 2

9 8 6 5 10 2 7 4 3 1

见题面 Input 部分

见题面 Output 部分