CodeForces 1017B - The Bits（思维）

Rudolf is on his way to the castle. Before getting into the castle, the security staff asked him a question:

Given two binary numbers a and b of length n. How many different ways of swapping two digits in a (only in a, not b) so that bitwise OR of these two numbers will be changed? In other words, let c be the bitwise OR of a and b, you need to find the number of ways of swapping two bits in a so that bitwise OR will not be equal to c.

Note that binary numbers can contain leading zeros so that length of each number is exactly n.

Bitwise OR is a binary operation. A result is a binary number which contains a one in each digit if there is a one in at least one of the two numbers. For example, 010102 OR 100112 = 110112.

Well, to your surprise, you are not Rudolf, and you don’t need to help him… You are the security staff! Please find the number of ways of swapping two bits in a so that bitwise OR will be changed.

Input

The first line contains one integer n (2≤n≤105) — the number of bits in each number.

The second line contains a binary number a of length n.

The third line contains a binary number b of length n.

Output

Print the number of ways to swap two bits in a so that bitwise OR will be changed.

Examples Input

5
01011
11001

Output

4

Input

6
011000
010011

Output

6

Note

In the first sample, you can swap bits that have indexes (1,4), (2,3), (3,4), and (3,5).

In the second example, you can swap bits that have indexes (1,2), (1,3), (2,4), (3,4), (3,5), and (3,6).

题目大意：给出两个二进制串a和b，询问交换a串中任意两个数后a | b的结果会不会改变，最后输出有几种交换方案能使a | b的值不同。

解题思路：这道题是一道思维题，我们需要考虑什么情况下按位或的值才会发生改变，按位或有四种情况：

• a=0,b=0 -> 0
• a=0,b=1 -> 1
• a=1,b=0 -> 1
• a=1,b=1 -> 1

我们发现只要有一个1最后结果就为1，我们讨论两种情况，

• b为0，a为0时，这时只要改边a的值为1 最后的值就会改变。
• b为0，a为1时，这时需要把a的值变为0 最后的值才会改变。

我们统计四个num，分别为前面提到过的四种情况

        if(a[i]=='0'&&b[i]=='0')
		  num1++;
		if(a[i]=='1'&&b[i]=='0')
		  num2++;
		if(a[i]=='1'&&b[i]=='1')
		  num3++;
		if(a[i]=='0'&&b[i]=='1')
		  num4++; 

对于第一种情况：a=0,b=0时，如果想让a变成1，我们去找a=1,b=0和a=1,b=1的情况。用num1（num2+num3）即可得到答案。
对于第二种情况：a=1,b=0时，想让a变成0，我们去找a=0,b=0和a=0,b=1的情况，因为a=0 b=0 和a=0 b=1已经交换过，所以只统计a=0 b=1，即num2 x num4 。最后让两种情况相加即可。AC代码：

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
using LL = long long;
string a,b;
int main()
{
	int n;
	cin>>n;
	cin>>a>>b;
	LL num1,num2,num3,num4;
	num1=num2=num3=num4=0;
	for(int i=0;i<n;i++)
	{
		if(a[i]=='0'&&b[i]=='0')
		  num1++;
		if(a[i]=='1'&&b[i]=='0')
		  num2++;
		if(a[i]=='1'&&b[i]=='1')
		  num3++;
		if(a[i]=='0'&&b[i]=='1')
		  num4++;    
	}
	LL ans=num1*(num2+num3)+num2*num4;
	cout<<ans<<endl;
	return 0;
}