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: Time Limit Exceeded)

function Main(input) {
    input = input.split("\n");
    var line;
    var cl = ["0,0"];
    var tmp = [];
    var result = [];
    var t;
    var dx;
    var dy;
    var final = "Yes";
    var start = 1;
    for(var i= 1; i <= parseInt(input[0], 10) ; i++){
        line = input[i].split(" ");
        t = line[0];
        dx = line[1];
        dy = line[2];
        for(var k = start; k <= parseInt( t , 10); k++){
            var len1 = cl.length;
            
            cl.forEach(function(cle, i) {
                var ax = cle.split(",")[0];
                var ay = cle.split(",")[1];
                
                tmp.push((parseInt(ax,10) + 1).toString() + "," + ay);
                if(parseInt(ax,10) - 1 >= 0){
                    tmp.push((parseInt(ax,10) - 1).toString() + "," + ay);
                }
                tmp.push(ax + "," + (parseInt(ay,10) + 1).toString());
                if(parseInt(ay,10) - 1 >= 0){
                    tmp.push(ax + "," + (parseInt(ay,10) - 1).toString());
                }
            });
            
            
            cl = tmp.concat();
            tmp.splice(0,tmp.length);
        }
        result[i] = "No";
        var len = cl.length;
        for(var l = 0; l <= len-1; l++){
            var x = cl[l].split(",")[0];
            var y = cl[l].split(",")[1];
            if(x === dx && y === dy){
                result[i] = "Yes";
                cl = [dx + "," + dy];
                start = parseInt(t,10)+1;
                break;
                
            }
        }
        if(result[i] === "No"){
            final = "No";
            break;
        }
    }
    //出力
    console.log(final);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));