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)

#if !defined(__clang__) && defined(__GNUC__)
#include <bits/stdc++.h>
#else
#include <cstdlib>
#include <climits>
#include <iostream>
#include <cstdint>
#include <vector>
#include <string>
#include <complex>
#include <bitset>
#include <queue>
#include <deque>
#include <stack>
#include <utility>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <regex>
#endif //  !defined(__clang__) && defined(__GNUG__)
#include <boost/lexical_cast.hpp>
#include <boost/algorithm/string.hpp>
#include <boost/multi_array.hpp>
#include <boost/optional.hpp>
#include <boost/math/common_factor_rt.hpp>

using namespace std;

template<typename T>
T absi(T x) {
    if (x < static_cast<T>(0)) {
        x *= static_cast<T>(-1);
    }
    return x;
}


int main()
{
    int64_t N;
    std::cin >> N;

    struct Pos {
        int64_t t;
        int64_t x;
        int64_t y;
    };

    std::vector<Pos> P;

    P.push_back({0, 0, 0});

    for (decltype(N) i = 0; i < N; ++i) {
        Pos t;
        std::cin >> t.t >> t.x >> t.y;
        P.push_back(t);
    }


    for (int64_t i = 1; i < P.size(); ++i) {
        auto diff_t = P[i].t - P[i-1].t;
        auto diff_x = absi(P[i].x - P[i-1].x);
        auto diff_y = absi(P[i].y - P[i-1].y);

        if (diff_t < diff_x + diff_y) {
            std::cout << "No" << std::endl;
            return 0;
        }
        auto rem = diff_t - (diff_x + diff_y);
        if (rem % 2 != 0) {
            std::cout << "No" << std::endl;
            return 0;
        }
    }
    std::cout << "Yes" << std::endl;

    return 0;
}