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

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

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.

***For Sample #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 $(2, 3, 1)$.

AtCoder [ABC276C]