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: Accepted)

class WeightedUnionFind:
    def __init__(self, n):
        self.n = n
        self.root = [-1]*(n+1)
        self.rnk = [-1]*(n+1)
        self.weight = [0]*(n+1)
    
    """ xの根を求める"""
    def Find_Root(self, x):
        if (self.root[x] < 0):
            return x
        else:
            y = self.Find_Root(self.root[x])
            self.weight[x] += self.weight[self.root[x]]
            self.root[x] = y
            return y
    
    """ 木の合併 """
    def Union(self, x, y, w):
        rx = self.Find_Root(x)
        ry = self.Find_Root(y)
        
        if self.rnk[rx] < self.rnk[ry]:
            self.root[rx] = ry
            self.weight[rx] = w - self.weight[x] + self.weight[y]
        
        else:
            self.root[ry] = rx
            self.weight[ry] = -w - self.weight[y] + self.weight[x]
            if self.rnk[rx] == self.rnk[ry]:
                self.rnk[rx] += 1
    
    """ xとyが同じ木に所属するかの判定 """
    def IsSameGroup(self, x, y):
        return self.Find_Root(x) == self.Find_Root(y)
    
    """ x,yのノード重みの取得 """
    def diff(self, x, y):
        return self.weight[x] - self.weight[y]
    
    """ xが属する木のサイズ(集合の個数)を取得 """
    def Size(self, x):
        return -self.root[self.Find_Root(x)]
n,m = map(int,input().split())
wuf = WeightedUnionFind(n)
flg = True
for _ in range(m):
    l,r,d = map(int,input().split())
    if not wuf.IsSameGroup(l,r):
        wuf.Union(l,r,d)
    else:
        if wuf.diff(l,r)!=d:
            flg = False
            break
print('Yes' if flg else 'No')