# Clairewd message

## Description

Clairewd is a member of FBI. After several years concealing in BUPT, she intercepted some important messages and she was preparing for sending it to ykwd. They had agreed that each letter of these messages would be transfered to another one according to a conversion table.
Unfortunately, GFW(someone’s name, not what you just think about) has detected their action. He also got their conversion table by some unknown methods before. Clairewd was so clever and vigilant that when she realized that somebody was monitoring their action, she just stopped transmitting messages.
But GFW knows that Clairewd would always firstly send the ciphertext and then plaintext(Note that they won’t overlap each other). But he doesn’t know how to separate the text because he has no idea about the whole message. However, he thinks that recovering the shortest possible text is not a hard task for you.
Now GFW will give you the intercepted text and the conversion table. You should help him work out this problem.

# 矩阵游戏

## Description

F[1][1]=1
F[i,j]=a×F[i][j-1]+b(j!=1)
F[i,1]=c×F[i-1][m]+d(i!=1)

# Matrix

## Description

Given an N*N matrix A, whose elements are either 0 or 1. A[i, j] means the number in the i-th row and j-th column. Initially we have A[i, j] = 0 (1 <= i, j <= N).

We can change the matrix in the following way. Given a rectangle whose upper-left corner is (x1, y1) and lower-right corner is (x2, y2), we change all the elements in the rectangle by using “not” operation (if it is a ‘0’ then change it into ‘1’ otherwise change it into ‘0’). To maintain the information of the matrix, you are asked to write a program to receive and execute two kinds of instructions.

1. C x1 y1 x2 y2 (1 <= x1 <= x2 <= n, 1 <= y1 <= y2 <= n) changes the matrix by using the rectangle whose upper-left corner is (x1, y1) and lower-right corner is (x2, y2).
2. Q x y (1 <= x, y <= n) querys A[x, y].

# Template

## 基本

• 普通青年
• 文艺青年
• 二逼青年

### $I/O$ 优化

• 一般读入优化
• $fread$
• 一般输出优化

## 数据结构

• 普通线段树
• 标记永久化

### 平衡树

• $fhq~Treap$
• 可持久化$Treap$(指针版$MLE$)
• 可持久化$Treap$(数组板$AC$)
• $splay$

## 图论

### 最短路

• $floyd$ 多源最短路 & 最短路径计数
• $spfa$ 单源最短路径
• $dijkstra$ 单源最短路径

### 最小生成树

• $kruskal$
• $prim$

### 网络流

• $dinic$ 网络流
• $zkw$ 最小费用最大流

## 数学基础

### $NTT$快速数论卷积

$r*2^k+1$ r k g
3 1 1 2
5 1 2 2
17 1 4 3
97 3 5 5
193 3 6 5
257 1 8 3
7681 15 9 17
12289 3 12 11
40961 5 13 3
65537 1 16 3
786433 3 18 10
5767169 11 19 3
7340033 7 20 3
23068673 11 21 3
104857601 25 22 3
167772161 5 25 3
469762049 7 26 3
998244353 119 23 3
1004535809 479 21 3
2013265921 15 27 31
2281701377 17 27 3
3221225473 3 30 5
75161927681 35 31 3
77309411329 9 33 7
206158430209 3 36 22
2061584302081 15 37 7
2748779069441 5 39 3
6597069766657 3 41 5
39582418599937 9 42 5
79164837199873 9 43 5
263882790666241 15 44 7
1231453023109121 35 45 3
1337006139375617 19 46 3
3799912185593857 27 47 5
4222124650659841 15 48 19
7881299347898369 7 50 6
31525197391593473 7 52 3
180143985094819841 5 55 6
1945555039024054273 27 56 5
4179340454199820289 29 57 3