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>
using namespace std;
int main() {
  int N;
  cin >> N ;
  int t = 0;
  int x = 0;
  int y = 0;
  int able = 0;
  for (int i = 0; i < N; i ++) {
    int ti, xi, yi;
    cin >> ti >> xi >> yi;
    int p = ti - t ;
    int q = max (xi - x, x - xi);
    int r = max (yi - y, y - yi);//pqrの定義
    if (p < q + r) break;
    for (int a = q; a <= p; a++) {
      int b = a - q;
      if (p < a + b) {
        able = 2;
        break;
      }
      for (int c = r; c <= p - a - b; c ++) {
        int d = c - r;
        if (a + b + c + d == p) {
          able = 1;
          t = ti;
          x += xi;
          y += yi;
          break;
        }
        if (able) break;
      }
      if (able) break;
      able = 2;
    }
    if (able != 1) break;
  }
  if (able == 1) cout << "Yes" << endl;
  else cout << "No" << endl;
}