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<iostream>
using namespace std;
//3s, 2s後にどこに入れるか書き出す

int main() {
    int n;
    cin >> n;
    int cnt = 0;
    int x[n + 1], y[n + 1], t[n + 1];
    for (int i = 1; i <= n; i++) {
        cin >> t[i] >> x[i] >> y[i];
    }
    //need t[n], so separate for
    for (int i = 1; i <= n; i++) {
        if (t[i] % 2 == 0) {
            if ((x[i] + y[i]) % 2 == 0 && y[n] >= - x[n] - t[n] && y[n] >= x[n] - t[n] && y[n] <= - x[n] + t[n] && y[n] <= x[n] + t[n]) {
                cnt++;
            }
        } else {
            if ((x[i] + y[i]) % 2 != 0 && y[n] >= - x[n] - t[n] && y[n] >= x[n] - t[n] && y[n] <= - x[n] + t[n] && y[n] <= x[n] + t[n]) {
                cnt++;
            }
        }
    }
    if (cnt == n) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
}