5183: Love Triangles
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
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题目描述
C. Love Triangles
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
There are many anime that are about "love triangles": Alice loves Bob, and Charlie loves Bob as well, but Alice hates Charlie. You are thinking about an anime which has n characters. The characters are labeled from 1 to n. Every pair of two characters can either mutually love each other or mutually hate each other (there is no neutral state).
You hate love triangles (A-B are in love and B-C are in love, but A-C hate each other), and you also hate it when nobody is in love. So, considering any three characters, you will be happy if exactly one pair is in love (A and B love each other, and C hates both A and B), or if all three pairs are in love (A loves B, B loves C, C loves A).
You are given a list of m known relationships in the anime. You know for sure that certain pairs love each other, and certain pairs hate each other. You're wondering how many ways you can fill in the remaining relationships so you are happy with every triangle. Two ways are considered different if two characters are in love in one way but hate each other in the other. Print this count modulo 1000000007.
You hate love triangles (A-B are in love and B-C are in love, but A-C hate each other), and you also hate it when nobody is in love. So, considering any three characters, you will be happy if exactly one pair is in love (A and B love each other, and C hates both A and B), or if all three pairs are in love (A loves B, B loves C, C loves A).
You are given a list of m known relationships in the anime. You know for sure that certain pairs love each other, and certain pairs hate each other. You're wondering how many ways you can fill in the remaining relationships so you are happy with every triangle. Two ways are considered different if two characters are in love in one way but hate each other in the other. Print this count modulo 1000000007.
Input
The first line of input will contain two integers n,m (3≤n≤100000, 0≤m≤100000).
The next m lines will contain the desc
).
Each pair of people will be described no more than once.
Output
Print a single integer equal to the number of ways to fill in the remaining pairs so that you are happy with every triangle modulo 1000000007.
Examples
Input
3 0
Output
4
Input
4 4 1 2 1 2 3 1 3 4 0 4 1 0
Output
1
Input
4 4 1 2 1 2 3 1 3 4 0 4 1 1
Output
0
Note
In the first sample, the four ways are to:
- Make everyone love each other
- Make 1 and 2 love each other, and 3 hate 1 and 2 (symmetrically, we get 3 ways from this).
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输出样例 复制