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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

var debug = false

var sc = bufio.NewScanner(os.Stdin)

func main() {
	var n int
	fmt.Scanf("%s", &n)
	var targets []string
	for i := 0; i < n; i++ {
		if sc.Scan() {
			targets = append(targets, sc.Text())
		}
	}

	res := GetAnswer(n, targets)
	fmt.Printf("%v\n", res)
}

// GetAnswer ...
func GetAnswer(n int, targets []string) string {
	prt("inputs: n:%v targets:%#v", n, targets)
	result := "No"
	stx := 0
	sty := 0
	count := 0
	pasttime := 0
	for _, t := range targets {
		prt("target: %v", t)
		tarr := getIntArray(t)
		// pos := math.Abs(float64((tarr[1] - stx) + (tarr[2] - sty)))
		pos := math.Abs(float64((tarr[1] - stx)) + math.Abs(float64((tarr[2] - sty))))
		prt("pos: %d", int(pos))
		if (tarr[0]-pasttime)%2 == int(pos)%2 && int(pos) <= (tarr[0]-pasttime) {
			count++
			stx = tarr[1]
			sty = tarr[2]
			pasttime += tarr[0]
		}
		prt("count: %d", count)
	}
	if n == count {
		result = "Yes"
	}
	return result
}

func getIntArray(str string) []int {
	strarr := strings.Split(str, " ")
	intarr := []int{}
	for _, st := range strarr {
		ti, _ := strconv.Atoi(st)
		intarr = append(intarr, ti)
	}
	return intarr
}

func prt(format string, inputs ...interface{}) {
	if debug {
		fmt.Printf(format+"\n", inputs...)
	}
}