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.split.map &:to_i
l=[];r=[];d=[]
for k in 0...m
v=gets.split.map &:to_i
l[k],r[k],d[k]=v[0],v[1],v[2]
end
x=[nil]*n
t=[0]
x[l[0]]=0
loop{
#10
c=0
  l.each{|i|
  if t.include?(i)
w=nil
    w=x[l[i]]+d[i] if x[l[i]]!=nil
    if x[r[i]]!=nil||w
      print("No")
      exit
    else
      x[r[i]]=w
#20
      l.delete_at(i)
      r.delete_at(i)
      d.delete_at(i)
      t<<l[i]
      c+=1
    end
end
}
  r.each{|i|
  if t.include?(i)
w=nil
    w=x[r[i]]-d[i] if x[r[i]]!=nil
#30
    if x[l[i]]!=nil||w
      print("No")
      exit
    else
      x[l[i]]=w
      l.delete_at(i)
      r.delete_at(i)
      d.delete_at(i)
      t<<r[i]
#40
      c+=1
    end
end
  }
if c==0
  if l==[]
    print("Yes")
    exit
  end
  for i in 0..l.size
    if x[i]==nil
      t=[i]
      x[i]=0
      break
    end
  end
end
}