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:
import sys
from collections import defaultdict

sys.setrecursionlimit(1000000)

N, M = map(int, sys.stdin.readline().split())
E = defaultdict(list)

for _ in range(M):
    l, r, d = map(int, sys.stdin.readline().split())
    l -= 1
    r -= 1
    E[l].append((r, d))
    E[r].append((l, -d))

xs = [None] * N

def dfs(i, x):
    xs[i] = x
    mi, ma = x, x
    for j, d in E[i]:
        if xs[j] is None:
            res = dfs(j, x + d)
            if res is None:
                return None
            else:
                mi2, ma2 = res
                mi = min(mi2, mi)
                ma = max(ma2, ma)
        else:
            if xs[j] - x != d:
                return None
    return mi, ma

for i in range(N):
    if xs[i] is None:
        res = dfs(i, 0)
        if res is None:
            break
        else:
            mi, ma = res
            if ma - mi > 1e9:
                break
else:
    print('Yes')
    sys.exit()
print('No')