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.*;

public class Main {
	static HashMap<Integer, ArrayList<Edge>> map = new HashMap<>();
	static boolean[] visited = new boolean[100000+1];
	static int[] x = new int[100000+1];
	static int[][] constraints = new int[200000][3];
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(); int m = sc.nextInt();
		for(int i=1; i<=n; i++) {
			map.put(i, new ArrayList<Edge>());
		}
		Arrays.fill(visited, false);
		for(int i=0; i<m; i++) {
			int from = sc.nextInt();
			int to = sc.nextInt();
			int d = sc.nextInt();
			map.get(from).add(new Edge(to, d));
			map.get(to).add(new Edge(from, -d));
			constraints[i][0] = from; constraints[i][1] = to; constraints[i][2] = d;
		}
		for(int i=1; i<=n; i++) {
			if(!visited[i]) {
				x[i] = 0;
				dfs(i);
			}
		}
		for(int i=0; i<m; i++) {
			int from = constraints[i][0];
			int to = constraints[i][1];
			int d = constraints[i][2];
			if(x[to]-x[from]!=d) {
				System.out.println("No"); return;
			}
		}
		System.out.println("Yes");
	}
	
	static void dfs(int v) {
		if(visited[v]) return;
		visited[v] = true;
		for(Edge e : map.get(v)) {
			if(!visited[e.to]) {
				x[e.to] = x[v] + e.c;
				dfs(e.to);
			}
		}
		return;
	}
	
	static class Edge {
		int to;
		int c;
		Edge(int to, int c) {
			this.to = to; this.c  =c;
		}
	}
	
	static int binarySearch(int[] A, int x) {
		int l = 0;
		int r = A.length;
		while(l<r) {
			int mid = (l+r)/2;
			if(A[mid] == x) return mid;
			else if(x<A[mid]) r = mid;
			else l = mid+1;
		}
		return -1;
	}
	
	static long upper_bound(int[] A, int b) {
		// bよりおおきい値がはじめて出てくるindexを返す
		return lower_bound(A, b+1);
	}

	static long lower_bound(int[] A, int b) {
		// b以上の値がはじめて出てくるindexを返す
		int lb=0;
		int ub=A.length;
		while(ub>lb) {
			int mid = (lb+ub)/2;
			if(A[mid]>=b) ub = mid;
			else lb = mid+1;
		}
		return lb;
	}
	
	// union find lib
	// usage:
	// 最初にinitを呼ぶ
	// root: 直接は呼ばないで
	// unite: まとめる
	// same: グループ判定
	static void init(int par[], int N) {
		for(int i=0; i<N; i++) {
			par[i] = i;
		}
	}
	
	static int root(int x, int [] par) {
		if(par[x] == x) {
			return x;
		} else {
			return (par[x] = root(par[x], par));
		}
	}
	
	static boolean same(int x, int y, int[] par) {
		return root(x, par) == root(y, par);
	}
	
	static void unite(int x, int y, int[] par) {
		x = root(x, par);
		y = root(y, par);
		if(x == y) return;
		par[x] = y;
	}
	
	// end union find lib
	
	// number lib
	
	static int max(int...ls) {
		int ans = Integer.MIN_VALUE;
		for(int i=0; i<ls.length; i++) {
			ans = Math.max(ans, ls[i]);
		}
		return ans;
	}
	
	static int min(int...ls) {
		int ans = Integer.MAX_VALUE;
		for(int i=0; i<ls.length; i++) {
			ans = Math.min(ans, ls[i]);
		}
		return ans;
	}
	
	static long lcm(long a, long b) {
		return a*(b/gcd(a, b));
	}
	
	static long gcd(long a, long b) {
		long ta = Math.max(a, b);
		long tb = Math.min(a, b);
		long tmp;
		while((tmp = ta%tb) != 0) {
			ta = tb;
			tb = tmp;
		}
		return tb;
	}
	
	static long modcomb(long n, long k, long mod) {
		if(k==1) {
			return n;
		}
		
		long ans = 1;
		for(long i=n; i>=n-k+1; i--) {
			ans = (ans * i)%mod;
		}
		for(long i=k; 0<i; i--) {
			ans = (ans * modpow(i, mod-2, mod)) % mod;
		}
		return ans;
	}
	
	static long modpow(long a, long b, long mod) {
		if(b==0) return 1;
		if(b%2==0) {
			long d = modpow(a, b/2, mod);
			return (d*d)%mod;
		} else {
			return (a*modpow(a, b-1, mod))%mod;
		}
	}
	
	static int disit(long a, long d) {
		int count = 0;
		while(a!=0) {
			a = a/d;
			count++;
		}
		return count;
	}
	
	// end number lib
}