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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
struct node{
    int to;
    int far;
};
vector<node> v[100000];
int x[100000];
bool done[100000];
bool dfs(int i,int now){
    done[i]=1;
    x[i]=now;
    for(auto itr:v[i]){
        if(!done[itr.to]){
            if(!dfs(itr.to,now+itr.far))return false;
        }else if(x[itr.to]!=x[i]+itr.far)return false;
    }
    return true;
};

int main(void){
    int n,m;
    bool a=true;
    cin>>n>>m;
    for(int i=0;i<m;i++){
        int l,r,d;
        cin>>l>>r>>d;
        v[l-1].push_back({r-1,d});
        v[r-1].push_back({l-1,-d});
    }
    for(int i=0;i<n;i++)if(!done[i])if(!dfs(i,0))a=0;
    string ans=(a)?"Yes":"No";
    cout<<ans<<endl;
}