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 JavaScript (node.js v5.12) (judge verdict: Accepted)

const main = () => {
  const txys = getParams()
      , txys_with_init = [[0,0,0], ...txys];
  console.log(solve(txys_with_init));
};

const getParams = () =>
  getStdin().split('\n').slice(1).map(s => s.split(' ').map(Number));

const getStdin = () =>
  require('fs').readFileSync('/dev/stdin', 'utf8').trim();

const solve = txys => {
  const pairs = zip(txys, txys.slice(1));
  return pairs.every(p => reachable(p[0], p[1])) ? 'Yes' : 'No';
};

const zip = (xs, ys) => {
  const minlen = Math.min(xs.length, ys.length);
  return [...Array(minlen).keys()].map(i => [xs[i], ys[i]]);
};

const reachable = (txy1, txy2) => {
  const t1 = txy1[0]
      , t2 = txy2[0]
      , x1 = txy1[1]
      , x2 = txy2[1]
      , y1 = txy1[2]
      , y2 = txy2[2]
      , difft = t2 - t1
      , distance = manhattanDistance(x1, x2, y1, y2);
  return enoughTime(difft, distance) && sameParity(difft, distance);
};

const manhattanDistance = (x1, x2, y1, y2) =>
  Math.abs(x1 - x2) + Math.abs(y1 - y2);

const enoughTime = (difft, distance) =>
  difft >= distance;

const sameParity = (m, n) =>
  m % 2 === n % 2;

main();