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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <numeric>
#include <bits/stdc++.h>
#include <utility>
#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>
#include <math.h>
#include <string>
#define ll long long
#define ull unsigned long long
#define make(type,x) type x; cin>>x
#define make2(type,x,y) type x,y; cin>>x>>y
#define fr(x,y) for(long long x=0;x<y;x++)
#define makevec(x,y,n) vector <x> y(n); for(ll i=0;i<n;i++) cin>>y[i]
#define M (ll)1000000007
#define MM (ll) 1e8
#define INF (ll) 1e18

# define IOS ios_base::sync_with_stdio(false); cin.tie(NULL)

using namespace std;

template <typename T>
T modpow(T base, T exp, T modulus) {
  base %= modulus;
  T result = 1;
  while (exp > 0) {
    if (exp & 1) result = (result * base) % modulus;
    base = (base * base) % modulus;
    exp >>= 1;
  }
  return result;
}
bool sortbysec(const pair <ll,ll> &a,const pair <ll,ll> &b){
    return a.second<b.second;
}

struct cmp {
	bool operator() (const pair<int, int> &a, const pair<int, int> &b) const {
		int lena = a.second - a.first + 1;
		int lenb = b.second - b.first + 1;
		if (lena == lenb) return a.first < b.first;
		return lena > lenb;
	}
};


struct c_h {
    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        x ^= FIXED_RANDOM;
        return x ^ (x >> 16);
    }
};

ll calcpow(ll x, ll y)
{
    ll temp;
    if(y == 0)
        return 1;
    temp = calcpow(x, y / 2);
    if (y % 2 == 0)
        return temp * temp;
    else
    {
        if(y > 0)
            return x * temp * temp;
        else
            return (temp * temp) / x;
    }
}
ll gcd(ll a, ll b){
    if(b==0) return a;
    return gcd(b,a%b);

}
ll egcd(ll a, ll b, ll &x,ll &y){
    if(b==0){
        x=1;
        y=0;
        return a;
    }
    ll x1;
    ll y1;
    ll g=egcd(b,a%b,x1,y1);
    x=y1;
    y=x1-y1*(a/b);
    return g;
}


bool isprime(ll a){
bool flag=1;
for(ll i=2;i*i<=a;i++){
    if(a%i==0) {flag=0; break;}
}
return flag;
}
ll n,m;
bool ok(ll a,ll b){
    return a>=0&&b>=0&&a<n&&b<m;
}
ll dx[8]={1,0,-1,0,1,-1,1,-1};
ll dy[8]={0,1,0,-1,1,-1,-1,1};

int main(){
    IOS;
    make(ll,n);
    vector <ll> t(n+1);
    vector <array <ll,2> >vec(n+1);
    fr(i,n) cin>>t[i+1]>>vec[i+1][0]>>vec[i+1][1];
    bool flag=1;
    for(ll i=1;i<n+1;i++){
        ll x=abs(vec[i][0]-vec[i-1][0])+abs(vec[i][1]-vec[i-1][1]);
        if(t[i]-t[i-1]<x || (t[i]-t[i-1]-x)%2==1) flag=0;
    }
    if(flag) cout<<"Yes \n";
    else cout<<"No \n";

    return 0;
}