Score : $500$ points

问题描述

我们有一个包含2行和$L$列的网格。令$(i,j)$表示从上数第$i$行（其中$i\in\lbrace1,2\rbrace$）且从左数第$j$列（$1\leq j\leq L$）的方格。在$(i,j)$上写有一个整数$x _ {i,j}$。

找出满足$x _ {1,j}=x _ {2,j}$的整数$j$的数量。

这里，对$x _ {i,j}$的描述以运行长度压缩的形式给出：分别将$(x _ {1,1},x _ {1,2},\ldots,x _ {1,L})$和$(x _ {2,1},x _ {2,2},\ldots,x _ {2,L})$压缩为长度分别为$N _ 1$和$N _ 2$的序列：$((v _ {1,1},l _ {1,1}),\ldots,(v _ {1,N _ 1},l _ {1,N _ 1}))$和$((v _ {2,1},l _ {2,1}),\ldots,(v _ {2,N _ 2},l _ {2,N _ 2}))$。

这里，序列$A$的运行长度压缩是指通过以下方式获得的一系列元素值$v _ i$和正整数$l _ i$构成的对$(v _ i,l _ i)$序列。

1. 在每对相邻不同元素之间分割$A$。
2. 对于分割后的每个子序列$B _ 1,B _ 2,\ldots,B _ k$，令$v _ i$为$B _ i$中的元素，$l _ i$为$B _ i$的长度。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have a grid with $2$ rows and $L$ columns. Let $(i,j)$ denote the square at the $i$-th row from the top $(i\in\lbrace1,2\rbrace)$ and $j$-th column from the left $(1\leq j\leq L)$. $(i,j)$ has an integer $x _ {i,j}$ written on it.

Find the number of integers $j$ such that $x _ {1,j}=x _ {2,j}$.

Here, the description of $x _ {i,j}$ is given to you as the run-length compressions of $(x _ {1,1},x _ {1,2},\ldots,x _ {1,L})$ and $(x _ {2,1},x _ {2,2},\ldots,x _ {2,L})$ into sequences of lengths $N _ 1$ and $N _ 2$, respectively: $((v _ {1,1},l _ {1,1}),\ldots,(v _ {1,N _ 1},l _ {1,N _ 1}))$ and $((v _ {2,1},l _ {2,1}),\ldots,(v _ {2,N _ 2},l _ {2,N _ 2}))$.

Here, the run-length compression of a sequence $A$ is a sequence of pairs $(v _ i,l _ i)$ of an element $v _ i$ of $A$ and a positive integer $l _ i$ obtained as follows.

1. Split $A$ between each pair of different adjacent elements.
2. For each sequence $B _ 1,B _ 2,\ldots,B _ k$ after the split, let $v _ i$ be the element of $B _ i$ and $l _ i$ be the length of $B _ i$.

Constraints

• $1\leq L\leq 10 ^ {12}$
• $1\leq N _ 1,N _ 2\leq 10 ^ 5$
• $1\leq v _ {i,j}\leq 10 ^ 9\ (i\in\lbrace1,2\rbrace,1\leq j\leq N _ i)$
• $1\leq l _ {i,j}\leq L\ (i\in\lbrace1,2\rbrace,1\leq j\leq N _ i)$
• $v _ {i,j}\neq v _ {i,j+1}\ (i\in\lbrace1,2\rbrace,1\leq j\lt N _ i)$
• $l _ {i,1}+l _ {i,2}+\cdots+l _ {i,N _ i}=L\ (i\in\lbrace1,2\rbrace)$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$L$ $N _ 1$ $N _ 2$

$v _ {1,1}$ $l _ {1,1}$

$v _ {1,2}$ $l _ {1,2}$

$\vdots$

$v _ {1,N _ 1}$ $l _ {1,N _ 1}$

$v _ {2,1}$ $l _ {2,1}$

$v _ {2,2}$ $l _ {2,2}$

$\vdots$

$v _ {2,N _ 2}$ $l _ {2,N _ 2}$

Output

Print a single line containing the answer.

Sample Input 1

8 4 3
1 2
3 2
2 3
3 1
1 4
2 1
3 3

Sample Output 1

4

The grid is shown below.

We have four integers $j$ such that $x _ {1,j}=x _ {2,j}$: $j=1,2,5,8$. Thus, you should print $4$.

Sample Input 2

10000000000 1 1
1 10000000000
1 10000000000

Sample Output 2

10000000000

Note that the answer may not fit into a $32$-bit integer.

Sample Input 3

1000 4 7
19 79
33 463
19 178
33 280
19 255
33 92
34 25
19 96
12 11
19 490
33 31

Sample Output 3

380

update @ 2024/3/10 12:14:42