CodeForces - 1110E-Magic Stones（差分+思维）

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探讨一个有趣的问题：是否存在一系列操作，使格里戈里的魔法石的电荷通过同步操作匹配安德鲁的石头电荷？文章详细解释了同步操作的过程，并提供了一个算法解决方案来判断是否可以实现电荷匹配。

Grigory has nn magic stones, conveniently numbered from 11 to nn. The charge of the ii-th stone is equal to cici.

Sometimes Grigory gets bored and selects some inner stone (that is, some stone with index ii, where 2≤i≤n−12≤i≤n−1), and after that synchronizes it with neighboring stones. After that, the chosen stone loses its own charge, but acquires the charges from neighboring stones. In other words, its charge cici changes to c′i=ci+1+ci−1−cici′=ci+1+ci−1−ci.

Andrew, Grigory's friend, also has nn stones with charges titi. Grigory is curious, whether there exists a sequence of zero or more synchronization operations, which transforms charges of Grigory's stones into charges of corresponding Andrew's stones, that is, changes cici into titi for all ii?

Input

The first line contains one integer nn (2≤n≤1052≤n≤105) — the number of magic stones.

The second line contains integers c1,c2,…,cnc1,c2,…,cn (0≤ci≤2⋅1090≤ci≤2⋅109) — the charges of Grigory's stones.

The second line contains integers t1,t2,…,tnt1,t2,…,tn (0≤ti≤2⋅1090≤ti≤2⋅109) — the charges of Andrew's stones.

Output

If there exists a (possibly empty) sequence of synchronization operations, which changes all charges to the required ones, print "Yes".

Otherwise, print "No".

Examples

Input

4
7 2 4 12
7 15 10 12

Output

Yes

Input

3
4 4 4
1 2 3

Output

No

Note

In the first example, we can perform the following synchronizations (11-indexed):

First, synchronize the third stone [7,2,4,12]→[7,2,10,12][7,2,4,12]→[7,2,10,12].
Then synchronize the second stone: [7,2,10,12]→[7,15,10,12][7,2,10,12]→[7,15,10,12].

In the second example, any operation with the second stone will not change its charge.

代码：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<queue>
#include<stack>
#include<vector>

using namespace std;

int a[100005],b[100005],c[100005],d[100005];
int main()
{
	int n;
	cin>>n;
	int flag=0;
	for(int t=1;t<=n;t++)
	{
		scanf("%d",&a[t]);
	}
	for(int t=1;t<=n;t++)
	{
		scanf("%d",&b[t]);
	}
	for(int t=1;t<=n-1;t++)
	{
		c[t]=a[t+1]-a[t];
	}
	for(int t=1;t<=n-1;t++)
	{
		d[t]=b[t+1]-b[t];
	}
	if(a[1]!=a[1]||a[n]!=b[n])
	{
		flag=1;
	}
	sort(c+1,c+n);
	sort(d+1,d+n);
	for(int t=1;t<=n;t++)
	{
		if(c[t]!=d[t])
		{
			flag=1;
		}
	}
	if(!flag)
	{
		puts("Yes");
	}
	else
	{
		puts("No");
	}
	
	return 0;
}