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.

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

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.

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.

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