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: Accepted)

package main
import (
   "fmt"
   "os"
   "bufio"
   "strconv"
   "math"
)
var sc = bufio.NewScanner(os.Stdin)

func main() {
  sc.Split(bufio.ScanWords)
  n := nextInt()
  x := 0.0
  y := 0.0
  t := 0
  var result []bool
  for i := 0; i < n; i++{
    ti := nextInt()
    xi := nextFloat()
    yi := nextFloat()
	t = ti - t
	abs := math.Abs(xi - x) + math.Abs(yi - y)
	if t % 2 == 0{
		if int(abs) <= t && int(abs)  % 2 == 0 {
			result = append(result, true)
		} else {
			result = append(result,false)
		}
	} else {
		if int(abs) <= t && int(abs)  % 2 == 1 {
			result = append(result, true)
		} else {
			result = append(result,false)
		}

	}
	t = ti
	x = xi
	y = yi
  }

  flg := true
  length  := len(result)
  for i := 0; i < length; i++ {
	  if result[i] == false {
		  flg = false
	  }
  }

  if flg {
	  fmt.Println("Yes")
  } else {
	  fmt.Println("No")
  }

}

func nextString() (string) {
	sc.Scan()
	v := sc.Text()
	return v
}

func nextInt() (int) {
	sc.Scan()
	v, e := strconv.Atoi(sc.Text())
    if e != nil { panic(e) }
    return v
}

func nextFloat() (float64) {
	sc.Scan()
	v, e := strconv.ParseFloat(sc.Text(), 64)
    if e != nil { panic(e) }
    return v
}