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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

class Main{

    static class Edge{
        int to,dis;
        Edge(int to,int dis){
            this.to = to;
            this.dis = dis;
        }
    }
    static int used[];
    static List<Edge> edgeList[];

    static boolean dfs(int v,int pos){
        if(used[v] > Integer.MIN_VALUE)return used[v] == pos;
        used[v] = pos;
        for(Edge e : edgeList[v]){
            if(!dfs(e.to,pos+e.dis))return false;
        }
        return true;
    }

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int M = scan.nextInt();
        edgeList = new ArrayList[N+1];
        for(int i=1;i<=N;++i)edgeList[i]=new ArrayList<>();
        used = new int[N+1];
        Arrays.fill(used,Integer.MIN_VALUE);
        for(int i=0;i<M;++i){
            int L = scan.nextInt();
            int R = scan.nextInt();
            int D = scan.nextInt();
            edgeList[L].add(new Edge(R,D));
            edgeList[R].add(new Edge(L,-D));
        }

        for(int i=1;i<=N;++i){
            if(used[i] > Integer.MIN_VALUE)continue;
            if(!dfs(i,0)){
                System.out.println("No");
                return;
            }
        }
        System.out.println("Yes");


    }
}