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: Accepted)

#include<iostream>
#include<string>
#include<vector>
#include<cmath>
#include<algorithm>
#include<cstdio>
#include<set>
#include<queue>
using namespace std;

typedef long long ll;

int t[100010];
int x[100010];
int y[100010];

int main() {
  int N; cin >> N;
  for ( int i  = 1; i <= N; i++ ) {
    cin >> t[i] >> x[i] >> y[i];
  }

  t[0] = x[0] = y[0] = 0;
  
  for ( int i = 0; i < N; i++ ) {
    int dis = abs(x[i+1]-x[i]) + abs(y[i+1] - y[i]);
    int tt = t[i+1]-t[i];
    // cout << "dis " << dis << " " << "tt " << tt << endl;
    if ( tt >= dis ) {
      if ( (dis % 2 == 1 && tt % 2 == 0)
	   || ( dis % 2 == 0 && tt % 2 == 1)) {
	cout << "No" << endl;
	return 0;
      }
    } else if ( tt < dis ) {
	cout << "No" << endl;
	return 0;      
    } else if ( dis == 0 ) {
      if (tt % 2 == 1 ) {
	cout << "No" << endl;
	return 0;      	
      }
    }
  }
  cout << "Yes" << endl;
  return 0;
}