CodeForces - 791B Bear and Friendship Condition

题意：

给你m对朋友关系，如果x-y是朋友,y-z是朋友，要求x-z也是朋友. 问你所给的图是否符合。

思路：

题意简单明了，就是判图中点与点的关系是否都是团。可以直接建图搜一圈。

也可以用并查集，参考：http://blog.csdn.net/harlow_cheng/article/details/63519393

搜索思路代码：

#include 

using namespace std;
const int MAXN = 2e5;
map  mp[MAXN];
vector  edge[MAXN];
bool vis[MAXN];
int que[MAXN],ppp;
int mlist[MAXN],pp,x,y;
long long n,m;
long long cut;
bool make_list(int pos){//....................列出团中的每个点
    pp=-1;
    int len=edge[pos].size();
    int now;
    cut+=len;
    for(int i=0;i>n>>m){
        for(int i=0;i>x>>y;
            mp[x][y]=1;
            mp[y][x]=1;
            edge[x].push_back(y);
            edge[y].push_back(x);
            vis[x]=1;vis[y]=1;
        }
        if(m>(n*(n+1)/2)){//..................剪枝，边的个数不会大于所有点都在一个团里的情况。
            cout<<"NO"<

Bear Limak examines a social network. Its main functionality is that two members can become friends (then they can talk with each other and share funny pictures).

There are n members, numbered 1 through n. m pairs of members are friends. Of course, a member can't be a friend with themselves.

Let A-B denote that members A and B are friends. Limak thinks that a network isreasonable if and only if the following condition is satisfied: For every threedistinct members (X, Y, Z), if X-Y and Y-Z then also X-Z.

For example: if Alan and Bob are friends, and Bob and Ciri are friends, then Alan and Ciri should be friends as well.

Can you help Limak and check if the network is reasonable? Print "YES" or "NO" accordingly, without the quotes.

Input

The first line of the input contain two integers n and m (3 ≤ n ≤ 150 000, ) — the number of members and the number of pairs of members that are friends.

The i-th of the next m lines contains two distinct integers a_i and b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). Members a_i and b_i are friends with each other. No pair of members will appear more than once in the input.

Output

If the given network is reasonable, print "YES" in a single line (without the quotes). Otherwise, print "NO" in a single line (without the quotes).

Example

Input

4 3
1 3
3 4
1 4

Output

YES

Input

4 4
3 1
2 3
3 4
1 2

Output

NO

Input

10 4
4 3
5 10
8 9
1 2

Output

YES

Input

3 2
1 2
2 3

Output

NO

Note

The drawings below show the situation in the first sample (on the left) and in the second sample (on the right). Each edge represents two members that are friends. The answer is "NO" in the second sample because members (2, 3) are friends and members(3, 4) are friends, while members (2, 4) are not.