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;
#define loop(I, N) for(int I = 1; I <= N; I++)
#define pool(I, N) for(int I = N; I >= 1; I--)
#define rep(I, N) for(int I = 0; I < N; I++)
#define per(I, N) for(int I = N - 1; I >= 0; I--)
#define FOR(I, L, R) for(int I = L; I <= R; I++)
#define FOD(I, R, L) for(int I = R; I >= L; I--)
#define SET(P, VAL) memset(P, VAL, sizeof(P));

int n, x[100005], y[100005], t[100005], cx = 0, cy = 0;
int main() {
	scanf("%d", &n);
	loop(i, n) scanf("%d%d%d", &t[i], &x[i], &y[i]);
	x[0] = y[0] = t[0] = 0;
	loop(i, n) {
		int dst = x[i] - x[i - 1] + y[i] - y[i - 1];
		if(dst <= t[i] - t[i - 1] && (t[i] - t[i - 1] - dst) % 2 == 0) continue;
		printf("No\n");
		return 0;
	}
	printf("Yes\n");
	return 0;
}