Problem: 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`.

Examples

Input

3 3
1 2 1
2 3 1
1 3 2


Output

Yes


Input

3 3
1 2 1
2 3 1
1 3 5


Output

No


Input

4 3
2 1 1
2 3 5
3 4 2


Output

Yes


Input

10 3
8 7 100
7 9 100
9 8 100


Output

No


Input

100 0


Output

Yes

Solution (in PYTHON3):

Solution:
from collections import defaultdict

class XUnionFind(object):

    def __init__(self):
        self.table = defaultdict(lambda:-1)
        self.dtable = defaultdict(lambda:0)

    def find(self, x):
        parent = self.table[x] 
        if parent < 0:
            return x, 0
        else:
            root, distance = self.find(parent)
            new_distance = distance + self.dtable[x]
            self.table[x] = root
            self.dtable[x] = new_distance
            return root, new_distance

    def union(self, x1, x2, d = 0):
        root1, distance1 = self.find(x1)
        root2, distance2 = self.find(x2)
        if root1 == root2:
            if distance2 - distance1 != d:
                return False
            return True
        if root1 < root2:
            self.table[root1] += self.table[root2]
            self.table[root2] = root1
            self.dtable[root2] = distance1 + d - distance2
        else:
            self.table[root2] += self.table[root1]
            self.table[root1] = root2
            self.dtable[root1] = distance2 - d - distance1
        return True

def solve(N, M, lrd):
    uf = XUnionFind()
    for l, r, d in lrd:
        rc = uf.union(l, r, d)
        if rc == False:
            return False
    return True
        

if __name__ == "__main__":
    N, M = [int(x) for x in input().split()]
    lrd = []
    for i in range(M):
        lrd.append([int(x) for x in input().split()])
    if solve(N, M, lrd):
        print("Yes")
    else:
        print("No")