311325: CF1970D2. Arithmancy (Medium)

D2. Arithmancy (Medium)time limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

The only difference between the versions of this problem is the maximum value of $n$.

Professor Vector is preparing to teach her Arithmancy class. She needs to prepare $n$ distinct magic words for the class. Each magic word is a string consisting of characters X and O. A spell is a string created by concatenating two magic words together. The power of a spell is equal to the number of its different non-empty substrings. For example, the power of the spell XOXO is equal to 7, because it has 7 different substrings: X, O, XO, OX, XOX, OXO and XOXO.

Each student will create their own spell by concatenating two magic words. Since the students are not very good at magic yet, they will choose each of the two words independently and uniformly at random from the $n$ words provided by Professor Vector. It is therefore also possible that the two words a student chooses are the same. Each student will then compute the power of their spell, and tell it to Professor Vector. In order to check their work, and of course to impress the students, Professor Vector needs to find out which two magic words and in which order were concatenated by each student.

Your program needs to perform the role of Professor Vector: first, create $n$ distinct magic words, and then handle multiple requests where it is given the spell power and needs to determine the indices of the two magic words, in the correct order, that were used to create the corresponding spell.

Interaction

This is an interactive problem.

First, your program should read a single integer $n$ ($1 \le n \le 30$), the number of magic words to prepare. Then, it should print $n$ magic words it has created, one per line. The magic words must be distinct, each magic word must have at least 1 and at most $30\cdot n$ characters, and each character must be either X or O. We will denote the $i$-th magic word you printed as $w_i$ ($1 \le i \le n$).

Then, your program should read a single integer $q$ ($1 \le q \le 1000$), the number of students in the class. Then, it should repeat the following process $q$ times, one per student.

For the $j$-th student, it should first read a single integer $p_j$, the power of their spell. It is guaranteed that this number is computed by choosing two indices $u_j$ and $v_j$ independently and uniformly at random between 1 and $n$ inclusive, concatenating $w_{u_j}$ and $w_{v_j}$, and finding the number of different non-empty substrings of the resulting string. Then, your program must print the numbers $u_j$ and $v_j$, in this order ($1 \le u_j, v_j \le n$).

Note that it is not enough to find any two magic words that concatenate into a spell with the given power. You must find the exact words used by the student in the exact order.

Remember to flush the output stream after printing all magic words and after printing $u_j$ and $v_j$ for each student.

ExampleInput

2


2
15

11

Output

XOXO
X


1 1

2 1

题目大意：
这个问题是关于生成具有特定“力量”的魔法词汇的。你需要编写一个程序，首先生成n个不同的魔法词汇，然后根据给定的“力量”值，确定用于创建相应咒语的魔法词汇的索引。

输入输出数据格式：
输入：
- 一个整数n（1 ≤ n ≤ 30），表示需要准备的魔法词汇的数量。
- 一个整数q（1 ≤ q ≤ 1000），表示班上的学生数量。
- 对于每个学生，一个整数p_j，表示他们咒语的力量。

输出：
- n个不同的魔法词汇，每个词汇至少有1个字符，最多有30*n个字符，且每个字符只能是'X'或'O'。
- 对于每个学生的询问，输出两个整数u_j和v_j，分别表示用于创建咒语的魔法词汇的索引，且u_j必须在v_j之前。

注意：每次输出后需要刷新输出流。题目大意： 这个问题是关于生成具有特定“力量”的魔法词汇的。你需要编写一个程序，首先生成n个不同的魔法词汇，然后根据给定的“力量”值，确定用于创建相应咒语的魔法词汇的索引。 输入输出数据格式： 输入： - 一个整数n（1 ≤ n ≤ 30），表示需要准备的魔法词汇的数量。 - 一个整数q（1 ≤ q ≤ 1000），表示班上的学生数量。 - 对于每个学生，一个整数p_j，表示他们咒语的力量。 输出： - n个不同的魔法词汇，每个词汇至少有1个字符，最多有30*n个字符，且每个字符只能是'X'或'O'。 - 对于每个学生的询问，输出两个整数u_j和v_j，分别表示用于创建咒语的魔法词汇的索引，且u_j必须在v_j之前。 注意：每次输出后需要刷新输出流。