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:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
from collections import deque
# people on a line
n, m = map(int, input().split())

graph = {i: {} for i in range(1, n + 1)}


for _ in range(m):
    a, b, c = map(int, input().split())
    graph[a][b] = c
    graph[b][a] = -c



distance = ["inf" for i in range(n + 1)]

# グラフにおいて順に点を決めてって、矛盾がないかどうかを調べる
visited = [False for i in range(n + 1)]
visited[0] = True


def find(x):
    d = deque()
    visited[x] = True
    distance[x] = 0
    d.append(x)
    flag = True
    while d and flag:

        x = d.popleft()
        for node in graph[x]:
            if visited[node] == False:
                visited[node] = True
                d.append(node)
                if distance[node] == "inf":
                    distance[node] = distance[x] + graph[x][node]
                else:
                    if  distance[node] != distance[x] + graph[x][node]:
                        flag = False
                        break
            elif visited[node]==True:
                if distance[node]!=distance[x]+graph[x][node]:
                    flag=False
                    break
         
    if flag:
        return False
    else:
        return True

all_flag = True
not_visited = True
while not_visited and all_flag:
    judge = False
    for i in range(1, n + 1):
        if visited[i] == False:
            judge = True
            if find(i):
                all_flag = False
                break
            else:
                pass

    if not judge:
        not_visited = False

if all_flag:
    print("Yes")

else:
    print("No")