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.*;
import java.io.*;


public class Main {
	
	public static class edge {
		
		node l;
		node r;
		int d;
		
		public edge(node l, node r, int d) {
			this.l = l;
			this.r = r;
			this.d = d;
		}
		
	}	
	public static class node {
		
		boolean assigned; //have we ever given this a val?
		LinkedList<edge> edg;
		boolean cleared; //processed
		int loc;
		
		public node() {
			assigned = false;
			loc = 0;
			cleared = false;
			edg = new LinkedList<edge>();
		}
	}
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] rd;
		rd = in.readLine().split("\\s++");
		int n = Integer.parseInt(rd[0]);
		int m = Integer.parseInt(rd[1]);
		node[] nodes = new node[n];
		for(int i = 0; i < n; i++) {
			nodes[i] = new node();
		}
		for(int i = 0; i < m; i++) {
			rd = in.readLine().split("\\s++");
			int l = Integer.parseInt(rd[0]);
			int r = Integer.parseInt(rd[1]);
			int d = Integer.parseInt(rd[2]);
			edge t = new edge(nodes[l-1], nodes[r-1], d);
			nodes[l-1].edg.offer(t);
			nodes[r-1].edg.offer(t);
		}
		boolean gucci = true;
		for(int i = 0; i < n; i++) {
			if(nodes[i].cleared) continue;
			LinkedList<node> q = new LinkedList<node>();
			q.offer(nodes[i]);
			nodes[i].assigned = true;
			while(!q.isEmpty()) {
				node nod = q.poll();
				for(edge e : nod.edg) {
					node oth = e.l;
					int dir = -1;
					if(e.l == nod) {
						oth = e.r;
						dir = 1;
					}
					if(oth.cleared) continue;
					else {
						if(!oth.assigned) {
							q.offer(oth);
							oth.loc = nod.loc + dir * e.d;
							oth.assigned = true;
						} else {
							if(oth.loc != nod.loc + dir * e.d) gucci = false;
						}
					}
				}
				nod.cleared = true;
			}
		}
		System.out.println(gucci ? "Yes" : "No");
	}
}