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>
using namespace std;
int fr[100005],nex[400005],vi[400005],wi[400005],tot=0;
void add(int x,int y,int z){
	nex[++tot]=fr[x];vi[tot]=y;wi[tot]=z;fr[x]=tot;
}
int n,m,vs[100005],d[100005];
void dfs(int x,int fa){
	vs[x]=1;
	for(int i=fr[x];i;i=nex[i])if(fa!=vi[i]){
		if(d[vi[i]]!=0x7f7f7f7f){
			if(wi[i]!=d[vi[i]]-d[x]){
				puts("No");exit(0);
			}
		}else{
			d[vi[i]]=d[x]+wi[i];
			dfs(vi[i],x);
		}
	}
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1,x,y,z;i<=m;++i){
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z);
		add(y,x,-z);
	}
	memset(d,0x7f,sizeof d);
	for(int i=1;i<=n;++i)if(!vs[i])dfs(i,i);
	puts("Yes");
	return 0;
}