Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in Python (3.4.3) (judge verdict: Runtime Error)

#!/usr/bin/python3
# -*- coding: utf-8 -*-

import sys

class G(object):
    def __init__(self, i):
        self.paths = dict()

    def add(self, v, d):
        self.paths[v] = d

    def dist(self, g, s):
        if self is g:
            return s
        if g in self.paths:
            d = g.dist(g, s + self.paths[g])
            self.add(g, d)
            return d
        for k, v in self.paths.items():
            d = k.dist(g, s + v)
            if d >= 0:
                self.add(v, d)
                return d
        return -1

def main():
    (n, m) = tuple(map(int, input().split()))
    lrds = tuple(map(int, input().split()) for _ in range(m))

    g = dict()
    for lrd in lrds:
        (l, r, d) = lrd
        if l not in g:
            g[l] = G(l)
        if r not in g:
            g[r] = G(r)
        pd = g[l].dist(g[r], 0)
        if pd != -1 and pd != d or g[r].dist(g[l], 0) != -1:
            print('No')
            sys.exit()
        g[l].add(g[r], d)

    print('Yes')

if __name__ == '__main__':
    main()