311324: CF1970D1. Arithmancy (Easy)

D1. Arithmancy (Easy)time limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

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 $n$ ($1 \le n \le 3$), 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：
_vector教授准备教授算术课。她需要为课程准备n个不同的魔法词。每个魔法词都是由字符X和O组成的字符串。一个咒语是通过连接两个魔法词创建的字符串。咒语的力量等于其不同非空子字符串的数量。例如，咒语XOXO的力量等于7，因为它有7个不同的子字符串：X、O、XO、OX、XOX、OXO和XOXO。_

_每个学生将通过连接两个魔法词来创建自己的咒语。由于学生们的魔法技能还不够好，他们将从vector教授提供的n个单词中独立且均匀地随机选择每个单词。因此，学生选择的两个单词也有可能是相同的。然后，每个学生将计算他们的咒语的力量，并将其告诉vector教授。为了检查他们的工作，当然还有给学生们留下深刻印象，vector教授需要找出每个学生连接的是哪两个魔法词以及它们的顺序。_

_程序需要扮演vector教授的角色：首先，创建n个不同的魔法词，然后处理多个请求，其中给出了咒语的力量，并需要确定用于创建相应咒语的两个魔法词的索引，以及正确的顺序。_

输入输出数据格式：
_输入：_
- 一个整数n（1≤n≤3），表示要准备的魔法词的数量。
- 一个整数q（1≤q≤1000），表示班上的学生数量。
- 每个学生的咒语力量pj。

_输出：_
- n个魔法词，每个词在一行中。
- 对于每个学生，输出两个整数uj和vj，表示创建该学生咒语的两个魔法词的索引，按顺序排列。题目大意： _vector教授准备教授算术课。她需要为课程准备n个不同的魔法词。每个魔法词都是由字符X和O组成的字符串。一个咒语是通过连接两个魔法词创建的字符串。咒语的力量等于其不同非空子字符串的数量。例如，咒语XOXO的力量等于7，因为它有7个不同的子字符串：X、O、XO、OX、XOX、OXO和XOXO。_ _每个学生将通过连接两个魔法词来创建自己的咒语。由于学生们的魔法技能还不够好，他们将从vector教授提供的n个单词中独立且均匀地随机选择每个单词。因此，学生选择的两个单词也有可能是相同的。然后，每个学生将计算他们的咒语的力量，并将其告诉vector教授。为了检查他们的工作，当然还有给学生们留下深刻印象，vector教授需要找出每个学生连接的是哪两个魔法词以及它们的顺序。_ _程序需要扮演vector教授的角色：首先，创建n个不同的魔法词，然后处理多个请求，其中给出了咒语的力量，并需要确定用于创建相应咒语的两个魔法词的索引，以及正确的顺序。_ 输入输出数据格式： _输入：_ - 一个整数n（1≤n≤3），表示要准备的魔法词的数量。 - 一个整数q（1≤q≤1000），表示班上的学生数量。 - 每个学生的咒语力量pj。 _输出：_ - n个魔法词，每个词在一行中。 - 对于每个学生，输出两个整数uj和vj，表示创建该学生咒语的两个魔法词的索引，按顺序排列。