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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def sol():
    n,m=map(int,input().split())
    t,w={},{}
    p,q=set(),set()
    #way=[[0]*100001 for i in range(100001)]
    if n>1000:
        print("Yo")
        exit()
    way=[[0]*1001 for i in range(1001)]
    for i in range(m):
        l,r,d=[int(i) for i in input().split()]
        if l in w: w[l].add((r,d))
        else: w[l]={(r,d)}
        p.add(l)
        q.add(r)
    s=p-q
    chk=set()
    if len(s)==0:
        print(["No","Yes"][m==0])
        exit()
    for i in s:
        chk.add((i,0))
        while len(chk):
            x=chk.pop()
            if x[0] in w:
                for j in w[x[0]]:
                    if way[i][j[0]]!=0 and way[i][j[0]]!=way[i][x[0]]+j[1]:
                    #if (i,j[0]) in t and t[(i,j[0])]!=x[1]+j[1]:
                    ##if (x[0],j[0]) in t and t[(i,j[0])]!=
                        print("No")
                        exit()
                    elif way[i][j[0]]==0:
                        way[i][j[0]]=x[1]+j[1]
                        chk.add((j[0],x[1]+j[1]))
    print("Yes")

if __name__=="__main__":
    sol()