Robot Rapping Results Report

84 阅读 0 评论 56 点赞

我是靠谱客的博主时尚小霸王，最近开发中收集的这篇文章主要介绍Robot Rapping Results Report，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

While Farmer John rebuilds his farm in an unfamiliar portion of Bovinia, Bessie is out trying some alternative jobs. In her new gig as a reporter, Bessie needs to know about programming competition results as quickly as possible. When she covers the 2016 Robot Rap Battle Tournament, she notices that all of the robots operate under deterministic algorithms. In particular, robot i will beat robot j if and only if robot i has a higher skill level than robot j. And if robot i beats robot j and robot j beats robot k, then robot i will beat robot k. Since rapping is such a subtle art, two robots can never have the same skill level.

Given the results of the rap battles in the order in which they were played, determine the minimum number of first rap battles that needed to take place before Bessie could order all of the robots by skill level.

Input

The first line of the input consists of two integers, the number of robots n (2 ≤ n ≤ 100 000) and the number of rap battles m ().

The next m lines describe the results of the rap battles in the order they took place. Each consists of two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), indicating that robot ui beat robot vi in the i-th rap battle. No two rap battles involve the same pair of robots.

It is guaranteed that at least one ordering of the robots satisfies all m relations.

Output

Print the minimum k such that the ordering of the robots by skill level is uniquely defined by the first k rap battles. If there exists more than one ordering that satisfies all m relations, output -1.

Examples

Input

Output

Input

3 2
1 2
3 2

Output

-1

Note

In the first sample, the robots from strongest to weakest must be (4, 2, 1, 3), which Bessie can deduce after knowing the results of the first four rap battles.

In the second sample, both (1, 3, 2) and (3, 1, 2) are possible orderings of the robots from strongest to weakest after both rap battles.

思路：拓扑排序，每次找入度为0的点并且只有一个，不会有多个。然后删除的时候记录最大的编号的边，如果能找到这个排序，输出答案。

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<iostream>
#include<algorithm>
using namespace std;
struct node
{
int u,v,next;
} e[100010];
int head[100010],cnt;
int n,m;
int q[100010];
int in[100010];
int main()
{
scanf("%d%d",&n,&m);
memset(head,-1,sizeof(head));
cnt=0;
memset(in,0,sizeof(in));
for(int i=0; i<m; i++)
{
int u,v;
scanf("%d%d",&u,&v);
e[cnt].u=u;
e[cnt].v=v;
e[cnt].next=head[u];
head[u]=cnt++;
in[v]++;
}
int ans=0;
int tail=0,flag=1;
for(int i=1; i<=n; i++)
if(in[i]==0)q[tail++]=i;
if(tail>1)flag=0;
for(int i=0; i<tail; i++)
{
int t=q[i];
int res=0;
for(int j=head[t]; j!=-1; j=e[j].next)
{
if(--in[e[j].v]==0)
{
q[tail++]=e[j].v;
res++;
ans=max(ans,j);
}
}
if(res>1)flag=0;
}
if(flag==0||tail<n)
cout<<-1<<endl;
else
cout<<ans+1<<endl;
return 0;
}