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)

import sys
N, M = map(int, input().split())
if M == 0:
    print('Yes')
    sys.exit()
m = []
for i in range(M):
    m.append(list(map(int, input().split())))
x = [None for i in range(N)]

def which_set(l, index):
    for i, ll in enumerate(l):
        if index in ll:
            return i
    return -1

lines = [set((m[0][0]-1, m[0][1]-1))]
x[m[0][0]-1] = 0
x[m[0][1]-1] = m[0][2]
for mm in m[1:]:
    l_set = which_set(lines, mm[0]-1)
    r_set = which_set(lines, mm[1]-1)
    if r_set >= 0 and l_set >=0 and r_set == l_set:
        if x[mm[1]-1] - x[mm[0]-1] == mm[2]:
            pass
        else:
            print('No')
            sys.exit()
    elif l_set >= 0 and r_set < 0:
        lines[l_set].add(mm[1]-1)
        x[mm[1]-1] = x[mm[0]-1] + mm[2]		
    elif l_set < 0 and r_set >= 0:
        lines[r_set].add(mm[0]-1)
        x[mm[0]-1] = x[mm[1]-1] - mm[2]
    elif r_set >= 0 and l_set >=0:
        lines[r_set].add(lines[l_set])
        d = x[mm[1] -1] - x[mm[0]-1]
        for i in lines[l_set]:
            x[i] += x[i] - d
        del lines[l_set]
    else:
        lines.append(set((mm[0]-1, mm[1]-1)))
        x[mm[0]-1] = 0
        x[mm[1]-1] = mm[2]

print('Yes')