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 <iostream>
using namespace std;

int main() {
    int N;
    int t[110000], x[110000], y[110000];
    cin >> N;
    t[0] = x[0] = y[0] = 0;  // 初期状態
    for (int i = 0; i < N; ++i) cin >> t[i+1] >> x[i+1] >> y[i+1];  // 1-index にしておく

    bool can = true;
    for (int i = 0; i < N; ++i) {
        int dt = t[i+1] - t[i];
        int dist = abs(x[i+1] - x[i]) + abs(y[i+1] - y[i]);
        if (dt < dist) can = false;
        if (dist % 2 != dt % 2) can = false;  // dist と dt の偶奇は一致する必要あり！
    }

    if (can) cout << "Yes" << endl;
    else cout << "No" << endl;
}