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:
from collections import deque
import sys
input = sys.stdin.readline

def bfs(graph, start):
    while graph != {}:
        start = min(graph.keys())
        queue = deque([])
        queue.append(start)
        pos = {}
        pos[start] = 0
        while queue:
            u = queue.popleft()
            for v,d in graph[u].items():
                if v not in pos:
                    pos[v] = pos[u] + d
                    if v in graph:
                        queue.append(v)
                elif pos[v] != pos[u] + d:
                    return False
            del graph[u]
            # print(queue)
    return True

n,m = map(int, input().split())

graph = {}
for i in range(m):
    l,r,d = map(int, input().split())
    if l not in graph:
        graph[l] = {}
    graph[l][r] = d
    if r not in graph:
        graph[r] = {}
    graph[r][l] = -d

if m == 0 or bfs(graph, min(graph.keys())):
    print('Yes')
else:
    print('No')
# print(graph)