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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <bits/stdc++.h>
using namespace std;

int main()
{
    long long x,y,t,i,j,n,xl,yl,cnt=0,tl,prod,trel;
    bool ok=1;
    cin>>n;
    cin>>tl>>xl>>yl;
    prod=xl+yl;
    if(xl==yl&&yl==0)
            prod=2;
    if(prod<=tl&&(prod<=n*n||prod<tl%(n*n)-1)){}
    else ok=0;
    if(xl>n||yl>n)
            ok=0;

    for(i=2;i<=n;i++)
    {
        cin>>t>>x>>y;
        if(x>n||y>n)
            ok=0;
        prod=fabs(x-xl)+fabs(y-yl);
        trel=fabs(t-tl);
        if(prod==0)
            prod=2;
        if(prod<=trel&&(trel<=n*n||prod<trel%(n*n)-1)){}
        else ok=0;
        xl=x;
        yl=y;
        tl=t;
    }
    if(ok==1)
        cout<<"Yes";
    else cout<<"No";
    return 0;
}