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: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define faster ios_base::sync_with_stdio(false); cin.tie(NULL);
#define ll long long
#define pb push_back
#define vi vector<int>
struct Node
{
    int t;
    int x;
    int y;
    Node(int a,int b, int c)
    {
        t = a;
        x = b;
        y = c;
    }
    bool operator<(const Node&ob) const
    {
        return t<ob.t;
    }
};
int main()
{
    faster;
    int n,t,x,y,a=0,b=0,tme=0;
    int ans = 1;
    cin>>n;
    vector<Node> v;
    for(int i=1; i<=n; i++){
        cin>>t>>x>>y;
        v.push_back(Node(t,x,y));
    }
    sort(v.begin(),v.end());
    for(int i=0; i<n; i++){
        t = v[i].t;
        x = v[i].x;
        y = v[i].y;
        if(t==tme && (a!=x || b!=y)) ans = 0;
        int dist = abs(x-a) + abs(y-b);
        if(dist>abs(tme-t)) ans = 0;
        else{
            int diff = abs(tme-t) - dist;
            if(diff%2==1) ans = 0;
        }
        a = x;
        b = y;
        tme = t;
    }
    if(ans==1) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}