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