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 {
	class Edge {
		int to, cost;

		public Edge(int to, int cost) {
			super();
			this.to = to;
			this.cost = cost;
		}

	}

	List<Edge>[] graph;
	boolean[] used;
	long[] pos;
	
	void dfs(int u, long p) {
		used[u] = true;
		pos[u] = p;
		for (int t = 0; t < graph[u].size(); t++) {
			Edge e = graph[u].get(t);
			if (!used[e.to]) {
				dfs(e.to, p + e.cost);
			} else if (pos[e.to] != p + e.cost){
				fail = true;
			}
		}
	}
	boolean fail = false;
	
	void solve() {
		int n = in.nextInt(), m = in.nextInt();
		graph = new List[n];
		for (int i = 0; i < n; i++) {
			graph[i] = new ArrayList<>();
		}
		for (int i =0; i < m; i++) {
			int from = in.nextInt() - 1, to =in.nextInt() - 1, len = in.nextInt();
			graph[from].add(new Edge(to, len));
			graph[to].add(new Edge(from, -len));
		}
		used = new boolean[n];
		pos = new long[n];
		for (int i = 0; i < n; i++) {
			if (!used[i]) {
				dfs(i, 0);
			}
		}
		out.println(fail ? "No" : "Yes");
	}

	FastScanner in;
	PrintWriter out;

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public String nextToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextToken());
		}

		public long nextLong() {
			return Long.parseLong(nextToken());
		}

		public double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}
}