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"
    "sort"
    "math"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {
    sc.Split(bufio.ScanWords)
    n := nextInt()
    m := [][]int{}
    m = append(m, []int{0,0,0})
    for i := 0; i < n; i++ {
        m = append(m, nextIntArr(3))
    }

    ans := "Yes"

    for i := 1; i < len(m); i++ {
        dt := int(math.Abs(float64(m[i-1][0] - m[i][0])))
        dx := int(math.Abs(float64(m[i-1][1] - m[i][1])))
        dy := int(math.Abs(float64(m[i-1][2] - m[i][2])))
        if dt < dx + dy || dt % (dx + dy) != 0 {
            ans = "No"
            break
        }
    }

    fmt.Println(ans)
}

func nextLine() string {
    sc.Scan()
    return sc.Text()
}

func nextInt() int {
    sc.Scan()
    i, _ := strconv.Atoi(sc.Text())
    return i
}

func nextIntArr(n int) []int {
    var a []int
    for i := 0; i < n; i++ {
        a = append(a, nextInt())
    }
    return a
}

// 数値を桁区切りのスライスにする
func digit(n int, list []int) []int {
   if n > 0 {
       return digit(n/10, append(list, n%10))
   }
   return list
}

func sortIntsRev(list []int) {
    sort.Sort(sort.Reverse(sort.IntSlice(list)))
}

func strReverse(s string) string {
    runes := []rune(s)
    for i := 0; i < len(s)/2; i++ {
        runes[i], runes[len(s)-1-i] = runes[len(s)-1-i], runes[i]
    }
    return string(runes)
}