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:
//ΔARC090B
#include<iostream>
#include<cstdio>
#include<fstream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<cmath>
#include<cstring>
#include<cstdlib>
using namespace std;
typedef long long LL;
typedef double DB;
const int N = 111111;
int n,m,a[N],vis[N];
vector<int> v[N],p[N];
void dfs(int u){
	int i,x,z;
	vis[u]=1;
	i=v[u].size();
	while(i--){
		x=v[u][i];
		z=p[u][i];
		if(vis[x]){
			if(a[x]!=a[u]+z){
				printf("No");
				exit(0);
			}
		}
		else{
			a[x]=a[u]+z;
			dfs(x);
		}
	}
}
int main()
{
	int i,x,y,z;
	scanf("%d%d",&n,&m);
	while(m--){
		scanf("%d%d%d",&x,&y,&z);
		v[x].push_back(y);
		p[x].push_back(z);
		v[y].push_back(x);
		p[y].push_back(-z);
	}
	for(i=1;i<=n;i=i+1)
		if(!vis[i])
			dfs(i);
	printf("Yes");
	return 0;
}