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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#define rep(i,n) for(int i=0;i<n;i++)
int gcd(int a, int b){
    int r=1;
    while(r!=0){
        r=a%b;
        a=b;
        b=r;
    }
    return a;
}
void revStr(char* str){
    int size = strlen(str);
    int i,j;
    char tmp = {0};
    for(i = 0, j = size - 1; i < size / 2; i++, j--){
        tmp = str[i];
        str[i] = str[j];
        str[j] = tmp;
    }return;
}
struct data{
    int a,b,c;
};

//降順
int compare_int(const void *a, const void *b)
{
    return *(int*)b - *(int*)a;
}
#define MAXSIZE 200000
int list[MAXSIZE];
int tail;

void Init(void){
    tail=0;
}
int Top(void){
    return 0;
}

int Next(int pos){
    if(pos<tail-1){
        return pos+1;
    }else{
        return -1;
    }
}
int Count(void){
    return tail;
}

int Item(int pos){
    if((pos>=0)&&(pos<tail)){
        return list[pos];
    }else{
        return 0;
    }
}
void Add(int value){
    if(tail<MAXSIZE){
        list[tail]=value;
        tail++;
    }
}
void Delete(int pos){
    if((pos>=0)&&(pos<tail)){
        int i;
        for(i=pos;i<tail-1;i++){
            list[i]=list[i+1];
        }
        tail--;
    }
}

int main(){
    int N;
    scanf("%d",&N);
    struct data whr[N];
    whr[0].a=0;whr[0].b=0;whr[0].c=0;
    for(int i=1;i<=N;i++){
        scanf("%d%d%d",&whr[i].a,&whr[i].b,&whr[i].c);
    }
    for(int i=0;i<N;i++){
        int sa=0;
        sa=(whr[i+1].a-whr[i].a);
        sa-=abs(whr[i+1].b-whr[i].b);
        if(sa<0){
            printf("No");
            return 0;
        }else{
            ;
        }
        sa-=abs(whr[i+1].c-whr[i].c);
        if(sa<0){
            printf("No");
            return 0;
        }else{
            ;
        }
        if(sa%2==1){
            printf("No");
            return 0;
        }else{
            ;
        }
    }
    printf("Yes");
    return 0;
}