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>
using namespace std;

const int maxn=1000005;

int fa[maxn];
int dis[maxn];

int Find(int x)
{
    if(fa[x]==x)
        return x;
    int r=Find(fa[x]);
    dis[x]=dis[fa[x]]+dis[x];
    return fa[x]=r;
}

int Union(int x,int y,int z)
{
    int fx=Find(x);
    int fy=Find(y);

    if (fx==fy)
        return z==dis[y]-dis[x];
    fa[fy]=fx;
    dis[fy]=dis[x]+z-dis[y];
    return 1;
}

int main()
{
    int n,m;
    int flag= 1;
    cin>>n>>m;
    for (int i=1;i<=n;i++)
        fa[i]=i;
    for (int i=1;i<=m;i++)
    {
        int l,r,d;
        cin>>l>>r>>d;
        if (flag)
            flag=Union(l,r,d);
    }
    if (flag)
        cout<<"Yes"<<endl;
    else
        cout<<"No"<<endl;
    return 0;
}