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
sys.setrecursionlimit(100000)
def depth_dp(v):
    if point[v] == float('inf'):
        point[v] = 0
    flag[v] = True
    for e in E[v]:
        if point[e[0]] == float('inf'):
            point[e[0]] = point[v] + e[1]
        elif point[e[0]] != point[v] + e[1]:
            return False
    for e in E[v]:
        if not flag[e[0]]:
            if not depth_dp(e[0]):
                return False
    return True

N,M = list(map(int,input().split()))
E = [[] for _ in range(N)]
flag = [False]*N
ans = True
point = [float('inf')]*N
for i in range(M):
    L,R,D = list(map(int,input().split()))
    E[L-1].append((R-1,D))
    E[R-1].append((L-1,-D))
for i in range(N):
    if not flag[i]:
        if not depth_dp(i):
            ans = False
            break
if ans:
    print('Yes')
else:
    print('No')