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)

//  cout << char(i+48) << endl;//なぜかaは47と得る時がある。+48で出力もaにできる。
//  cout << char(97) << endl;//アスキーコードでaを出力
// sort(b.begin(), b.end());//bという配列を小さい方からソート
// reverse(b.begin(), b.end());//bという配列をリターン
// 10桁でdouble出力するパターン１ 
// printf("%.10f\n", ma);
// 10桁でdouble出力するパターン２
//cout << fixed << setprecision(10);
//  cout << ma << endl;

/*01 02 03 12 13 23　と６回見ていくパターン 
for(int i=0;i<n-1;i++){
  for(int j=i+1;j<n;j++){
    }
  }
*///vector<vector<int>> data(3, vector<int>(4));//int型の2次元配列(3×4要素の)の宣言
//int64_t a;
//10のi乗pow(10, i);
/*string s; stringでの文字列を数字型に変える方法
  cin >> s;
  rep(i,s.size()-2) {
  int a= (s.at(i)-'0')*100 + (s.at(i+1)-'0')*10+ s.at(i+2) -'0';
    */
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
int main() {
  int n;
  cin >> n;
  vector<int>t(n+1);
  vector<int>x(n+1);
  vector<int>y(n+1);
  for(int i = 1;i<n+1;i++){
  cin >> t.at(i) >> x.at(i) >> y.at(i);
  }
  int flag=0;
  int kyori = 0;
  int time = 0;
  for(int i = 1;i<n+1;i++){
    kyori = abs(x.at(i)-x.at(i-1))+abs(y.at(i)-y.at(i-1));
    time =  abs(t.at(i)-t.at(i-1));
    if(kyori > time){
      flag = 1;
      break;
    }
    if(kyori%2 != time%2){
      flag = 1;
      break;
    }
  }
  if(flag==1) cout<<"No"<<endl;
  else cout<<"Yes"<<endl;
}