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.Scanner;
import java.util.*;
 
public class Main {
	public static ArrayList <Integer>linkList[][];
	public static int dists[];
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		linkList = new ArrayList[N + 1][2];
		dists = new int[N + 1];
		
		for(int i = 0; i < N + 1; i++) {
			dists[i] = Integer.MIN_VALUE;
			linkList[i][0] = new ArrayList<Integer>();
			linkList[i][1] = new ArrayList<Integer>();
		}
		for(int i = 0; i < M; i++) {
			int l = sc.nextInt();
			int r = sc.nextInt();
			int d = sc.nextInt();
			linkList[l][0].add(r);
			linkList[l][1].add(d);
			linkList[r][0].add(l);
			linkList[r][1].add(-d);
		}
		for(int i = 0; i < N; i++){
			if(dists[i] != Integer.MIN_VALUE)continue;
			if(!dfs(i, 0)){
				System.out.println("No");
				return;
			}
		}
		System.out.println("Yes");
	}
	public static boolean dfs(int i, int dist) {
		if(dists[i] != Integer.MIN_VALUE)return dists[i] == dist;
		dists[i] = dist;
		for(int j = 0; j < linkList[i][0].size(); j++) {
			if(!dfs(linkList[i][0].get(j), dist + linkList[i][1].get(j)))return false;
		}
		return true;
	}
}