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 <bits/stdc++.h>
using namespace std;
using ll = long long;
using edge = struct {int to; ll cost;};

#define mod 1000000007
#define REP(i, n) for (int i = 0; i < n; i++)
#define INF (1 << 29)


void solve() {
    int n;
    cin >> n;
    int X = 0, Y = 0;
    int T = 0;
    int t[n], x[n], y[n];
    REP(i, n) cin >> t[i] >> x[i] >> y[i];
    REP(i, n){
        int minCost = abs(X - x[i]) + abs(Y - y[i]);
        int Time = t[i] - T;
        if(Time < minCost || (Time - minCost) % 2 != 0) {
            cout << "No" << "\n";
            return;
        }
        X = x[i];
        Y = y[i];
        T = t[i];
    }
    cout << "Yes" << "\n";
}

int main() {
    solve();
    return 0;
}