Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1 ≤ N ≤ 10^5

0 ≤ x_i ≤ 10^5

0 ≤ y_i ≤ 10^5

1 ≤ t_i ≤ 10^5

t_i < t_{i+1} (1 ≤ i ≤ N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t_1 x_1 y_1
t_2 x_2 y_2
:
t_N x_N y_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

Sample Input 2

1
2 100 100

Sample Output 2

No

It is impossible to be at (100,100) two seconds after being at (0,0).

Sample Input 3

2
5 1 1
100 1 1

Sample Output 3

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

int main()
{int N;
 vector<int> t(N), x(N), y(N);
  for(int i = 0; i < N ; i++)
 { cin >> t[i] >> x[i] >> y[i];}
 
 vector<int> s(N), X(N), Y(N);
 s[0] = t[0];X[0] = x[0]; Y[0] = y[0];
 for(int i = 1; i < N; i++)
 {s[i] = t[i] - t[i-1];
  X[i] = x[i] - x[i-1];
  Y[i] = y[i] - y[i-1];}
 //差分vectorを作った
 
 bool big_flag = true;
 for(int j = 0; j < N; j++)
 { bool flag = false;
   int Z = abs(X[j]) + abs(Y[j]);
 if( Z % 2 == 0 && s[j] % 2 == 0 && Z <= s[j]){flag = true;}
  else if(Z % 2 == 1 && s[j] % 2 == 1 && Z <= s[j]){flag = true;}
  if(!flag){big_flag = false;
    break;}}
 
 if(big_flag){cout << "Yes" << endl;}
 else{cout << "No" << endl;}
 return 0;
}