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: Wrong Answer)

import sys 

temp=input().split(" ")
n=int(temp[0])
m=int(temp[1])
# p=[[-1 for i in range(n)] for j in range(n)]
p=[]
dis=[-1]*(n+1)
for i in range(m):
    temp=input()
    p.append(temp)
p.sort()
if m!=0:
    temp=p[0].split(" ")
    x=int(temp[0])
    y=int(temp[1])

    d=int(temp[2])
    dis[x]=0
    dis[y]=d

    p.pop(0)

    for temp in p:
        temp=temp.split(" ")
        x=int(temp[0])
        y=int(temp[1])    
        d=int(temp[2])
        if dis[x]==-1 and dis[y]==-1: #完全な新情報なら
            dis[x]=0
            dis[y]=d
        elif dis[x]==-1: #xだけ不明なら
            dis[x]=dis[y]-d
        elif dis[y]==-1:
            dis[y]=dis[x]+d
        if dis[y]!=dis[x]+d:
            # print (x)
            # print (y)
            # print (d)
            print("No")
            sys.exit()
print("Yes")