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++ (GCC 9.2.1) (judge verdict: Accepted)

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include <algorithm>
#include <iostream>

using namespace std;

const int MAX_N = 1E+05;

int N;
int scdl[MAX_N][3];

bool solve();

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> N;

    for (int i = 0; i < N; i++) {
        cin >> scdl[i][0] >> scdl[i][1] >> scdl[i][2];
    }

    if (solve()) {
        cout << "Yes\n";
    } else {
        cout << "No\n";
    }
    return 0;
}

bool solve()
{
    int t = 0;
    int x = 0;
    int y = 0;
    for (int i = 0; i < N; i++) {
        int dt = scdl[i][0] - t;
        t = scdl[i][0];
        int dx = abs(scdl[i][1] - x);
        x = scdl[i][1];
        int dy = abs(scdl[i][2] - y);
        y = scdl[i][2];

        bool cantra = false;
        for (; dt >= 0; dt -= 2) {
            if (dx + dy == dt) {
                cantra = true;
            }
        }
        if (!cantra)
            return false;
    }
    return true;
}