###### Description

Suppose that there is a country that consists of `N`

towns. A number between 1 and `N`

is given to each town. They are connected with the bi-directional roads, and when someone wants to move between different towns, he/she must pass the road. It takes different time to pass according to the road. At this point, a restaurant at the town 1 is going to deliver the food to each town. Among `N`

towns, the restaurant wants to receive the order from towns where delivery can be done with less than `K`

time. The following is an example when `N`

= 5 and `K`

= 3.

In the above figure, the restaurant at the town 1 can deliver the food to the town [1, 2, 4, 5] with less than 3 time. But, since there is no way to deliver food th town 3 with less than 3 times, the restaurant does not receive an order from town 3. Therefore, the number of towns where the restaurant at the town 1 receives an order is 4.

Given the number of towns `N`

, the information of road that connects each town `road`

, and the target delivery time `K`

as parameters, write a function `solution`

to return the number of towns where the restaurant accepts an order.

##### Constraints

- The number of towns
`N`

is a natural number between 1 and 50. - Length of
`road`

(the number of road's information) is between 1 and 2,000. - Each element of
`road`

indicates the information of each road that connects the towns. `road`

is an array with a length of 3, and represents (a, b) in turn.- a and b (1 ≤ a, b ≤
`N`

, a != b) are the town's number that connected by the road, and c (1 ≤ c ≤ 10,000, c is a natural number) indicates the time required to pass the road. - There may be several roads connecting town a and b.
- The information of a road is not given more than twice.

- a and b (1 ≤ a, b ≤
`K`

represents the time where food can be delivered and is between 1 and 500,000.- There is always path to move between any of two towns.
- Return the number of towns where the restaurant at town 1 can deliver the food with less than
`K`

time.

##### Examples

N | road | K | result |
---|---|---|---|

5 | [[1,2,1],[2,3,3],[5,2,2],[1,4,2],[5,3,1],[5,4,2]] | 3 | 4 |

6 | [[1,2,1],[1,3,2],[2,3,2],[3,4,3],[3,5,2],[3,5,3],[5,6,1]] | 4 | 4 |

Example #1

This is the same with the example in the problem statement.

Example #2

Given towns and roads are as shown in the following figure.

Since the number of towns where the delivery can be done with less than 4 times is 4, town [1, 2, 3, 5], return 4.