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 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#define MAX_N 100000

int delta_t(int *t) {
  return abs(t[1] - t[0]);
}

int mh_distance(int *x, int *y) {
  return abs(x[1] - x[0]) + abs(y[1] - y[0]);
}

char *yes_no(int *t, int *x, int *y, int N) {
  int i;
  for(i = 0; i <= N; i++) {
    int cur_t[2] = {t[i], t[i+1]};
    int cur_x[2] = {x[i], x[i+1]};
    int cur_y[2] = {y[i], y[i+1]};
    int d_t = delta_t(cur_t);
    int mh_d = mh_distance(cur_x, cur_y);
    if (d_t < mh_d || d_t % 2 != mh_d % 2) {
      return "No";
    }
  }
  return "Yes";
}

int main() {
  int i, N;
  scanf("%d", &N);
  int t[MAX_N]={0}, x[MAX_N]={0}, y[MAX_N]={0};
  for(i = 1; i <= N; i++) {
    scanf("%d %d %d", &t[i], &x[i], &y[i]);
  }
  char *result = yes_no(t, x, y, N);
  printf("%s", result);
  return 0;
}