You have just arrived in a new city and would like to see its sights. Each sight is located in a square and you have assigned each a beauty value. Each road to a square takes an amount of time to travel, and you have limited time for sightseeing. Determine the maximum value of beauty that you can visit during your time in the city. Start and finish at your hotel, the location of sight zero.

Output

43

Explanation : 0 -> 3 -> 0

Explanation:

Constraints

1 <= n <= 1000

1 <= m <= 2000

10 <= max_t <= 100

0 <= u[i], v[i] <= n-1

u[i] != v[i]

10 <= t[i] <= 100

0 <= beauty[i] <= 10^8

No more than 4 roads connect a single square with others

Two roads can be connected by at most 1 road

Example

n = 4

m = 3

max_t = 30

beauty = [5, 10, 15, 20]

u = [0, 1, 0]

v = [1, 2, 3]

t = [6, 7, 10]

Output

43

Explanation : 0 -> 3 -> 0

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wpe

wpe

wpe

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