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.io.*;
import java.lang.reflect.WildcardType;
import java.nio.file.ClosedWatchServiceException;
import java.nio.file.OpenOption;
import java.security.SecureRandom;
import java.util.*;

public class Main {
    public static void main(String[] args) throws FileNotFoundException {
        ConsoleIO io = new ConsoleIO(new InputStreamReader(System.in), new PrintWriter(System.out));
        //String test = "C-large";
        //ConsoleIO io = new ConsoleIO(new FileReader("D:\\Dropbox\\code\\practice\\jb\\src\\" + test + ".in"), new PrintWriter(new File("D:\\Dropbox\\code\\practice\\jb\\src\\" + test + "-out.txt")));

        new Main(io).solve();

        io.close();
    }

    ConsoleIO io;
    Main(ConsoleIO io) {
        this.io = io;
    }

    List<List<Edge>> gr = new ArrayList<>();
    long MOD = 1_000_000_007;

    public void solve() {
        int n = io.ri();
        int m = io.ri();
        for(int i = 0;i<n;i++)
            gr.add(new ArrayList<>());
        for(int i= 0;i<m;i++) {
            int left = io.ri()-1, right = io.ri()-1;
            int d = io.ri();
            Edge e = new Edge(left, right, d);
            gr.get(left).add(e);
            gr.get(right).add(e);
        }
        coord = new int[n];
        boolean res = true;
        for(int i = 0;i<n && res;i++)if(coord[i] == 0){
            coord[i] = (int)MOD;
            res&=go(i);
        }

        io.writeLine(res?"Yes":"No");
    }

    int[] coord;

    boolean go(int node) {
        List<Edge> ch = gr.get(node);
        int v = coord[node];
        for (int i = 0; i < ch.size(); i++) {
            Edge e = ch.get(i);
            int d = e.dist;
            int next = e.to;
            if (e.to == node) {
                d = -d;
                next = e.from;
            }
            int y = v + d;
            if (coord[next] != 0) {
                if (coord[next] != y)
                    return false;
            } else {
                coord[next] = y;
                if(!go(next))
                    return false;
            }
        }
        return true;
    }

    class Edge{
        public Edge(int left, int right, int d){
            from = left;
            to = right;
            dist = d;
        }
        public int from;
        public int to;
        public int dist;
    }
}

class ConsoleIO {

    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(Reader reader, PrintWriter writer){br = new BufferedReader(reader);out = writer;}
    public void flush(){this.out.flush();}
    public void close(){this.out.close();}
    public void writeLine(String s) {this.out.println(s);}
    public void writeInt(int a) {this.out.print(a);this.out.print(' ');}
    public void writeWord(String s){
        this.out.print(s);
    }
    public void writeIntArray(int[] a, int k, String separator) {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < k; i++) {
            if (i > 0) sb.append(separator);
            sb.append(a[i]);
        }
        this.writeLine(sb.toString());
    }
    public int read(char[] buf, int len){try {return br.read(buf,0,len);}catch (Exception ex){ return -1; }}
    public String readLine() {try {return br.readLine();}catch (Exception ex){ return "";}}
    public long[] readLongArray() {
        String[]n=this.readLine().trim().split("\\s+");long[]r=new long[n.length];
        for(int i=0;i<n.length;i++)r[i]=Long.parseLong(n[i]);
        return r;
    }
    public int[] readIntArray() {
        String[]n=this.readLine().trim().split("\\s+");int[]r=new int[n.length];
        for(int i=0;i<n.length;i++)r[i]=Integer.parseInt(n[i]);
        return r;
    }
    public int[] readIntArray(int n) {
        int[] res = new int[n];
        char[] all = this.readLine().toCharArray();
        int cur = 0;boolean have = false;
        int k = 0;
        boolean neg = false;
        for(int i = 0;i<all.length;i++){
            if(all[i]>='0' && all[i]<='9'){
                cur = cur*10+all[i]-'0';
                have = true;
            }else if(all[i]=='-') {
                neg = true;
            }
            else if(have){
                res[k++] = neg?-cur:cur;
                cur = 0;
                have = false;
                neg = false;
            }
        }
        if(have)res[k++] = neg?-cur:cur;
        return res;
    }
    public int ri() {
        try {
            int r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public long readLong() {
        try {
            long r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public String readWord() {
        try {
            boolean start = false;
            StringBuilder sb = new StringBuilder();
            while (true) {
                int c = br.read();
                if (c!= ' ' && c!= '\r' && c!='\n' && c!='\t') {
                    sb.append((char)c);
                    start = true;
                } else if (start || c == -1) return sb.toString();
            }
        } catch (Exception ex) {
            return "";
        }
    }
    public char readSymbol() {
        try {
            while (true) {
                int c = br.read();
                if (c != ' ' && c != '\r' && c != '\n' && c != '\t') {
                    return (char) c;
                }
            }
        } catch (Exception ex) {
            return 0;
        }
    }
    //public char readChar(){try {return (char)br.read();}catch (Exception ex){ return 0; }}
}
class Pair {
    public Pair(int a, int b) {this.a = a;this.b = b;}
    public int a;
    public int b;
}
class PairLL {
    public PairLL(long a, long b) {this.a = a;this.b = b;}
    public long a;
    public long b;
}
class Triple {
    public Triple(int a, int b, int c) {this.a = a;this.b = b;this.c = c;}
    public int a;
    public int b;
    public int c;
}