CodeForces 634A-Island Puzzle【找规律】

Love The Way You Lie 2022-08-21 00:20 124阅读 0赞

A. Island Puzzle

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A remote island chain contains *n* islands, labeled 1 through *n*. Bidirectional bridges connect the islands to form a simple cycle — a bridge connects islands 1 and 2, islands  2 and 3, and so on, and additionally a bridge connects islands *n* and 1. The center of each island contains an identical pedestal, and all but one of the islands has a fragile, uniquely colored statue currently held on the pedestal. The remaining island holds only an empty pedestal.

The islanders want to rearrange the statues in a new order. To do this, they repeat the following process: First, they choose an island directly adjacent to the island containing an empty pedestal. Then, they painstakingly carry the statue on this island across the adjoining bridge and place it on the empty pedestal.

Determine if it is possible for the islanders to arrange the statues in the desired order.

Input

The first line contains a single integer *n* (2 ≤ *n* ≤ 200 000) — the total number of islands.

The second line contains *n* space-separated integers *a**i* (0 ≤ *a**i* ≤ *n* - 1) — the statue currently placed on the *i*\-th island. If *a**i* = 0, then the island has no statue. It is guaranteed that the *a**i* are distinct.

The third line contains *n* space-separated integers *b**i* (0 ≤ *b**i* ≤ *n* - 1) — the desired statues of the *i*th island. Once again, *b**i* = 0 indicates the island desires no statue. It is guaranteed that the *b**i* are distinct.

Output

Print "YES" (without quotes) if the rearrangement can be done in the existing network, and "NO" otherwise.

Examples

Input

3
    1 0 2
    2 0 1

Output

YES

Input

2
    1 0
    0 1

Output

YES

Input

4
    1 2 3 0
    0 3 2 1

Output

Note

In the first sample, the islanders can first move statue  1 from island 1 to island  2, then move statue 2 from island  3 to island 1, and finally move statue  1 from island 2 to island  3.

In the second sample, the islanders can simply move statue  1 from island 1 to island  2.

In the third sample, no sequence of movements results in the desired position.

解题思路：

题目大意是有N座岛，我们可以假设这些岛是横向顺次连接的，并且最后一个岛和第一个岛也是相连的，现在这个数列中有一个0，它的作用就是0可以和相邻的两个位置上的数字互换位置从而到达和下面数列相同的状态。

多试几组数据我们会发现，其实零不加入到数组中，因为不管怎么移动，除一之外其他的数都会是一个顺序，只不过开始的坐标不同，for example 1230，可以变成0231，所以我们只需要找到第二个数组中第一个数组的第一个数的下标，在第二数组遍历一遍。

#include<stdio.h>
    #include<string.h>
    #include<algorithm>
    using namespace std;
    int a[10000+200000],b[200000+10000];
    int main()
    {
    	int n;
    	while(scanf("%d",&n)!=EOF)
    	{
    		int i,j=0;
    		for(i=0;i<n;i++)
    		{
    			int x;
    			scanf("%d",&x);
    			if(x==0)
    			{
    				continue;
    			}
    			a[j++]=x;
    		}
    		int pos;
    		j=0;
    		for(i=0;i<n;i++)
    		{
    			int x;
    			scanf("%d",&x);
    			if(x==0)
    			continue;
    			b[j++]=x;
    			if(x==a[0])
    			{
    				pos=j-1; 
    			}
    		}
    		bool f=false;
    		for(i=0;i<n-1;i++)
    		{
    			if(a[i]!=b[(i+pos)%(n-1)])
    			f=true;
    		}
    		if(f)
    		{
    			printf("NO\n");
    		}
    		else
    		printf("YES\n");
    	}
    	return 0;
    }