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<cstdio>
#include<iostream>
#include<vector>
#include<queue>
#include<bitset>
#include<string>
#include<stack>
#include<set>
#include<map>
#include<cstring>
#include<complex>
#include<cmath>
#include<algorithm>
#include<list>
#include<functional>
#define mp make_pair
#define X first
#define Y second
#define INF 1987654321
#define PI 3.14159265358979323846264
#define MOD 1000000007LL
#define fup(i,a,b,c) for(int (i)=(a);(i)<=(b);(i)+=(c))
#define fdn(i,a,b,c) for(int (i)=(a);(i)>=(b);(i)-=(c))
#define MEM0(a) memset(a,0,sizeof(a));
#define MEM_1(a) memset(a,-1,sizeof(a));
#define ALL(a) a.begin(),a.end()
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int, int> Pi;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
typedef vector<int> Vi;
typedef vector<ll> Vll;
typedef vector<double> Vd;
typedef vector<Pi> VPi;
typedef vector<Pll> VPll;
typedef vector<Pd> VPd;
typedef tuple<int, int, int> iii;
typedef complex<double> base;
ll POW(ll a, ll b) { if (b == 0)return 1; if (b == 1)return a; if (b & 1)return (a*POW(a, b - 1)) % MOD; ll t = POW(a, b / 2); return (t*t) % MOD; }
int gcd(int a, int b) { return b ? gcd(b, a%b) : a; }
int dx[] = { 0,-1,1,0 }, dy[] = { 1,0,0,-1 };//동북남서
int ddx[] = { 0,0,1,1,1,-1,-1,-1 }, ddy[] = { 1,-1,1,0,-1,1,0,-1 };

iii a[100001];
int dist(Pi p1, Pi p2)
{
	return (int)abs(p2.X - p1.X) + (int)abs(p2.Y - p1.Y);
}
int main() {
	int n;
	scanf("%d", &n);
	a[0] = iii(0, 0, 0);
	fup(i, 1, n, 1)
	{
		int t, x, y;
		scanf("%d%d%d", &t, &x, &y);
		a[i] = iii(t, x, y);
	}
	fup(i, 1, n, 1)
	{
		int t1, x1, y1, t2, x2, y2;
		tie(t1, x1, y1) = a[i - 1];
		tie(t2, x2, y2) = a[i];
		int T = t2 - t1;
		int d = dist(Pi(x1, y1), Pi(x2, y2));
		if (T < d)
		{
			puts("No");
			return 0;
		}
		if (T % 2 != d % 2)
		{
			puts("No");
			return 0;
		}
	}
	puts("Yes");
}