Previous Permutation

AtCoder

IDabc276_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ $P_1$ $\ldots$ $P_N$ [samples]

Samples

Input #1

3
3 1 2

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 $(2, 3, 1)$.

Input #2

10
9 8 6 5 10 3 1 2 4 7

Output #2

9 8 6 5 10 2 7 4 3 1

API Response (JSON)

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