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 <vector>
#include <string>
#include <algorithm>
#include <math.h>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <iomanip>
#include <map>
#include <utility>
#include <numeric>
#include <typeinfo>

using namespace std;

int main(){
  int N;
  cin >> N;
  vector<int> t(N+1);
  vector<int> x(N+1);
  vector<int> y(N+1);
  t.at(0)=0;
  x.at(0)=0;
  y.at(0)=0;
  for(int i=1;i<N+1;i++)  cin >> t.at(i) >> x.at(i) >> y.at(i);

  bool flag=true;
  for(int i=1;i<N+1;i++){
    int tim=t.at(i)-t.at(i-1);
    int dis=abs(x.at(i)-x.at(i-1)) + abs(y.at(i)-y.at(i-1));
    if(tim<dis) flag=false;
    else if((tim-dis)%2!=0) flag=false;
  }

  if(flag)  cout << "Yes" << endl;
  else  cout << "No" << endl;

  return 0;
}