Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

n, m = gets.chomp.split(" ").map(&:to_i)

if m == 0 then
    puts "Yes"
    exit
end

h = {}
m.times do
    l, r, d = gets.chomp.split(" ").map(&:to_i)

    h[l] = [] if h[l] == nil
    h[l] << [r, d]
    h[r] = [] if h[r] == nil
    h[r] << [l, -d]
end

p = Array.new(n+1, nil)
checked = Array.new(n+1, false)
p[1] = 0

def dfs(p, h, i, checked)
    if checked[i] == true
        return
    else
        checked[i] = true
    end

    if h[i] == nil
        puts "No"
        exit
    end
    return if h[i].size == 0
    h[i].each do |r, d|
        if p[r] != nil && p[r] - p[i] != d
            puts "No"
            exit
        end
        p[r] = p[i] + d
        dfs(p, h, r, checked)
    end
end

dfs(p, h, 1, checked)

puts "Yes"