Flame of Nucleus

Year 20XX — a nuclear explosion has burned the world. Half the people on the planet have died. Fearful.

One city, fortunately, was not directly damaged by the explosion. This city consists of N domes (numbered 1 through N inclusive) and M bidirectional transportation pipelines connecting the domes. In dome i, P_i citizens reside currently and there is a nuclear shelter capable of protecting K_i citizens. Also, it takes D_i days to travel from one end to the other end of pipeline i.

It has been turned out that this city will be polluted by nuclear radiation in L days after today. So each citizen should take refuge in some shelter, possibly traveling through the pipelines. Citizens will be dead if they reach their shelters in exactly or more than L days.

How many citizens can survive at most in this situation?

Input

The input consists of multiple test cases. Each test case begins with a line consisting of three integers N, M and L (1 ≤ N ≤ 100, M ≥ 0, 1 ≤ L ≤ 10000). This is followed by M lines describing the configuration of transportation pipelines connecting the domes. The i-th line contains three integers A_i, B_i and D_i (1 ≤ A_i < B_i ≤ N, 1 ≤ D_i ≤ 10000), denoting that the i-th pipeline connects dome A_i and B_i. There is at most one pipeline between any pair of domes. Finally, there come two lines, each consisting of N integers. The first gives P₁ , . . ., P_N (0 ≤ P_i ≤ 10⁶) and the second gives K₁ , . . ., K_N (0 ≤ K_i ≤ 10⁶).

The input is terminated by EOF. All integers in each line are separated by a whitespace.

Output

For each test case, print in a line the maximum number of people who can survive.

Sample Input

1 0 1
51
50
2 1 1
1 2 1
1000 0
0 1000
4 3 5
1 2 4
1 3 1
3 4 2
0 1000 1000 1000
3000 0 0 0

Output for the Sample Input

50
0
3000

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