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:
class DSUWeighted():
    def __init__(self, n):
        self.n = n
        self.par_size = [-1] * n
        self.wt = [0] * n

    def leader(self, a):
        #assert 0 <= a < self.n
        x = a
        order = [x]
        while self.par_size[x] >= 0:
            x = self.par_size[x]
            order.append(x)
        for s in order[:-1][::-1]:
            self.wt[s] += self.wt[self.par_size[s]]
            self.par_size[s] = x
        return x

    def same(self, a, b):
        #assert 0 <= a < self.n
        #assert 0 <= b < self.n
        return self.leader(a) == self.leader(b)

    def merge(self, a, b, w):
        #assert 0 <= a < self.n
        #assert 0 <= b < self.n
        x = self.leader(a)
        y = self.leader(b)
        w += self.wt[a] - self.wt[b]
        if x == y: return x
        if -self.par_size[x] < -self.par_size[y]:
            x, y = y, x
            w = -w
        self.par_size[x] += self.par_size[y]
        self.par_size[y] = x
        self.wt[y] = w
        return x

    def diff(self, x, y):
        return self.wt[y] - self.wt[x]

import sys
input = sys.stdin.buffer.readline

N, M = map(int, input().split())

uf = DSUWeighted(N)

for _ in range(M):
    l, r, d = map(int, input().split())
    if uf.same(l - 1, r - 1):
        if uf.diff(l - 1, r - 1) != d:
            print('No')
            break
    else:
        uf.merge(l - 1, r - 1, d)
else:
    print('Yes')