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)

#include<bits/stdc++.h> 
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
using namespace std;
using ll = long long;
using ull = unsigned long long;
using vv = vector<vector<int>>;
using P = pair<int,int>;

int main(){
  ll n;
  cin >> n;
  vector<vector<ll>> p(n,vector<ll>(3));
  rep(i,n) rep(j,3) cin >> p.at(i).at(j);
  sort(p.begin(),p.end());
  
  ll x=0,y=0,t=0;
  rep(i,n){
    t = p.at(i).at(0) - t;
    ll dis = abs(p.at(i).at(1)-x) + abs(p.at(i).at(2) - y);
    if( abs(t-dis)%2 != 0 || t < dis ){
      cout << "No" << endl;
      return 0;
    }
    x = p.at(i).at(1);
    y = p.at(i).at(2);
  }
  
  cout << "Yes" << endl;
  
  return 0;
}