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)

function main(input) {
    input = input.split("\n").map(e => e.split(" ").map(ee => Number(ee)))
    const N = input[0][0]
    input.shift()
    let T = 0, X = 0, Y = 0
    let count = 0
    for (arr of input) {
        let t = arr[0], x = arr[1], y = arr[2]
        const diffx = Math.abs(x - X)
        const diffy = Math.abs(y - Y)
        const difft = Math.abs(t - T)
        const sum = Math.abs(x + y)
        if ((diffx + diffy <= difft) && (t % 2 == sum % 2)) {
            count += 1
        }
        T = t
        X = x
        Y = y
    }
    const mes = count==N ? "Yes" : "No"
    console.log(mes)
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));