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:
N, M = map(int, input().split())
X = [list(map(int, input().split())) for _ in range(M)]

class WeightedUnionFind:
    def __init__(self, n):
        self.par = list(range(n))
        self.rank = [0] * n
        self.weight = [0] * n
        
    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            y = self.find(self.par[x])
            self.weight[x] += self.weight[self.par[x]]
            self.par[x] = y
            return y
        
    def unite(self, x, y, w):
        px = self.find(x)
        py = self.find(y)
        
        if px == py:
            return True
        
        if self.rank[px] == self.rank[py]:
            self.rank[px] += 1
        elif self.rank[px] < self.rank[py]:
            px, py = py, px
            x, y = y, x
            w *= -1

        self.par[py] = px
        self.weight[py] = self.weight[x] - self.weight[y] - w
                
    def same(self, x, y):
        return self.find(x) == self.find(y)
    
    def diff(self, x, y):
        return self.weight[x] - self.weight[y]

t = WeightedUnionFind(N + 1)
for l, r, d in X:
    if t.same(l, r):
        if t.diff(l, r) != d:
            print('No')
            break
    else:
        t.unite(l, r, d)
else:
    print('Yes')