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: Wrong Answer)

// ------------------------------------
// Date:2018/ 2/18
// Problem:ABC 086 Traveling c.cpp
//
// ------------------------------------

#include <bits/stdc++.h>

using namespace std;

#define EACH(i,a) for (auto&& i : a)
#define FOR(i,a,b) for(int i=(int)a;i<(int)b;++i)
#define RFOR(i,a,b) for(int i=(int)b-1;i>=(int)a;--i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)

int main()
{
  int N,dt,dx,dy,d;
  cin >> N;
  vector<int> t(N),x(N),y(N);
  REP(i,N) {
    cin >> t[i] >> x[i] >> y[i];
  }
  REP(i,N-1) {
    {
      dt = t[i+1]-t[i];
      dx = abs(x[i]-x[i+1]);
      dy = abs(y[i]-y[i+1]);
    }
    d = dx + dy;
    if (d%2 != dt%2) break;
    if (i == N-2) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}