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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define BUF_SIZE 20

struct point {
  int t;
  int x;
  int y;
};

int comp(const void* a, const void* b) {
  struct point* pa = (struct point*)a;
  struct point* pb = (struct point*)b;
  return pa->t - pb->t;
}

int is_move(struct point* cur, struct point* next) {
  int dist = abs(cur->x - next->x) + abs(cur->y - next->y);
  int time_diff = next->t - cur->t;
  if(time_diff < dist) return 0;
  if((dist&1) == (time_diff&1)) return 1;
  return 0;
}

int main(void) {
  FILE *fp = stdin;
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, fp)) return 0;

  int num;
  sscanf(line, "%d", &num);
  struct point *ps = malloc(sizeof(struct point)*(num+1));
  
  int i;
  ps[0].t = ps[0].x = ps[0].y = 0;
  for(i = 1; i <= num; i++) {
    if(!fgets(line, BUF_SIZE, fp)) return 0;
    sscanf(line, "%d %d %d", &ps[i].t, &ps[i].x, &ps[i].y);
  }
  // already sorted
  // qsort(ps, num+1, sizeof(struct point), comp);

  int flag = 1;
  for(i = 0; i < num; i++) {
    flag &= is_move(&ps[i], &ps[i+1]);
    if(!flag) break;
  }
  printf("%s\n", flag ? "Yes" : "No");
  return 0;
}