Problem: There are N people standing on the x-axis. Let the coordinate of Person i be x_i. For every i, x_i is an integer between 0 and 10^9 (inclusive). It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people. The i-th piece of information has the form (L_i, R_i, D_i). This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

* 1 \leq N \leq 100 000
* 0 \leq M \leq 200 000
* 1 \leq L_i, R_i \leq N (1 \leq i \leq M)
* 0 \leq D_i \leq 10 000 (1 \leq i \leq M)
* L_i \neq R_i (1 \leq i \leq M)
* If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).
* D_i are integers.

Input

Input is given from Standard Input in the following format:


N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M


Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print `Yes`; if it does not exist, print `No`.

Examples

Input

3 3
1 2 1
2 3 1
1 3 2


Output

Yes


Input

3 3
1 2 1
2 3 1
1 3 5


Output

No


Input

4 3
2 1 1
2 3 5
3 4 2


Output

Yes


Input

10 3
8 7 100
7 9 100
9 8 100


Output

No


Input

100 0


Output

Yes

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define N 500005
using namespace std;
int head[N],d[N]; bool vis[N],flag=false;
int n,m,x,y,z,kk=0;
struct Edge{int nxt,to,step;}e[N];
void link(int x,int y,int z){e[++kk].nxt=head[x];e[kk].to=y;e[kk].step=z;head[x]=kk;}
void dfs(int u)
{
	if (flag) return; vis[u]=true;
	for (int i=head[u];i;i=e[i].nxt){
		int v=e[i].to; if (flag) return;
		if (d[u]+e[i].step<d[v]){
			d[v]=d[u]+e[i].step;
			if (vis[v]){flag=true;return;}
			else dfs(v);
		}
	} vis[u]=false;
}
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=m;i++){
		scanf("%d%d%d",&x,&y,&z);
		link(x,y,z);link(y,x,-z);
	} flag=false;
	for (int i=1;i<=n;i++){
		dfs(i); if (flag) break;
	} if (flag) puts("No"); else puts("Yes");
	return 0;
}