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:
# 重み付きUnion-Findデータ構造
class WeightedUnionFind:
    def __init__(self, numV):
        self.pars = list(range(numV))
        self.ranks = [0] * numV
        self.weights = [0] * numV

    def find(self, x):
        if self.pars[x] == x:
            return x
        else:
            parXOld = self.pars[x]
            self.pars[x] = self.find(parXOld)
            self.weights[x] += self.weights[parXOld]
            return self.pars[x]

    def union(self, x, y, wt):
        wtX = self.getWeight(x)
        wtY = self.getWeight(y)
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return wtY == wtX+wt
        wt += wtX - wtY
        if self.ranks[x] < self.ranks[y]:
            self.pars[x] = y
            self.weights[x] = -wt
        else:
            self.pars[y] = x
            self.weights[y] = wt
            if self.ranks[x] == self.ranks[y]:
                self.ranks[x] += 1
        return True

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def getWeight(self, x):
        self.find(x)
        return self.weights[x]

    def getDiff(self, x, y):
        if self.find(x) == self.find(y):
            return self.getWeight(y) - self.getWeight(x)
        else:
            return float('inf')


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

WUF = WeightedUnionFind(N)
ans = 'Yes'
for _ in range(M):
    L, R, D = map(int, input().split())
    if not WUF.union(L-1, R-1, D):
        ans = 'No'

print(ans)