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: Runtime Error)

input = input.split(/\n/).slice(1).map(v => v.split(/\s/).map(v => ~~v))//

        let ans = 'Yes' // 'Yes' or 'No'
        let distance = 0 // distance
        let time = 0 // time
        let nextPosi = { x: 0, y: 0 }
        let nextTime = 0
        let tmpPosi = { x: 0, y: 0 }
        let tmpTime = 0

        for (let i = 0; i < input.length; i++) {

            nextPosi.x = input[i][1]
            nextPosi.y = input[i][2]

            distance = nextPosi.x - tmpPosi.x + nextPosi.y - tmpPosi.y

            nextTime = input[i][0]
            time = nextTime - tmpTime
            console.log(time % 2, distance % 2)
            if (distance > time) {// || time % 2 != distance % 2

                ans = 'No'
                break;
            }

            tmpTime = nextTime
            tmpPosi.x = nextPosi.x
            tmpPosi.y = nextPosi.y


        }

        console.log(ans)