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 <cmath>
#include <cstdio>

#include <stack>
#include <queue>
#include <algorithm>
#include <iostream>
#include <vector>
#include <map>
#include <numeric>
#include <string>
#include <array>

#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define all(x) x.begin(), x.end()

using namespace std;
typedef long long int ll;

struct txy{
  ll t;
  ll x;
  ll y;
};

int main() {
  ll n;
  cin >> n;
  vector<txy> a(n+1);
  a.at(0).t=0;
  a.at(0).x=0;
  a.at(0).y=0;
  rep(i, n) cin >> a.at(i+1).t >> a.at(i+1).x >> a.at(i+1).y;
  bool isCan = true;
  rep(i, n){
    if(not isCan) break;
    ll dir = abs(a.at(i).y-a.at(i+1).y)+abs(a.at(i).x-a.at(i+1).x);
    ll tim = a.at(i+1).t-a.at(i).t;
    if(dir <= tim){
      isCan = dir%2 ==0;
      if(tim%2==1) isCan = not isCan;
    }else{
      isCan = false;
    }
  }
  if (isCan)cout << "Yes" << endl;
  else cout << "No" << endl;
  return 0;
}