The sky darkens... it is raining geese. Oli is on a strip of land that is units long. He initially starts at unit on the left, and every second he can teleport **an integer** from to units, either left or right. He cannot travel beyond unit or beyond unit on the strip. squadrons of geese will rain from the sky. The th squadron hits the ground in seconds from now, **temporarily** vaporizing the area stretching from units to inclusive. Can he avoid all the geese without getting vaporized? The strip when is shown below.

#### Constraints

#### Input Specification

The first line of input contains space-separated integers, , , and .

The next lines each contain space-separated integers, , , and . These will be sorted in increasing order of , all times are distinct.

#### Output Specification

Output a single line containing `YES`

if he can survive and `NO`

if he cannot.

#### Sample Input 1

```
1000 2 1
300 600 1000
0 400 1001
```

#### Sample Output 1

`YES`

#### Sample Input 2

```
10 6 1
0 4 11
3 7 12
8 10 13
1 2 15
4 9 16
1 7 17
```

#### Sample Output 2

`YES`

#### Sample Input 3

```
5 3 3
0 0 1
2 5 2
0 4 3
```

#### Sample Output 3

`NO`

## Comments