题目描述

有N(1 <= N <= 200)个农场，用1..N编号。航空公司计划在农场间建立航线。对于任意一条航线，选择农场1..K中的农场作为枢纽(1 <= K <= 100, K <= N)。

当前共有M (1 <= M <= 10,000)条单向航线连接这些农场，从农场u_i 到农场 v_i, 将花费 d_i美元。(1 <= d_i <= 1,000,000).

航空公司最近收到Q (1 <= Q <= 10,000)个单向航行请求。第i个航行请求是从农场a_i到农场 b_i，航行必须经过至少一个枢纽农场（可以是起点或者终点农场），因此可能会多次经过某些农场。

请计算可行航行请求的数量，及完成所有可行请求的总费用。

输入格式

* Line 1: Four integers: N, M, K, and Q.

* Lines 2..1+M: Line i+1 contains u_i, v_i, and d_i for flight i.

* Lines 2+M..1+M+Q: Line 1+M+i describes the ith trip in terms of a_i and b_i

输出格式

* Line 1: The number of trips (out of Q) for which a valid route is possible.

* Line 2: The sum, over all trips for which a valid route is possible, of the minimum possible route cost.

3 3 1 3 
3 1 10 
1 3 10 
1 2 7 
3 2 
2 3 
1 2 

2 
24 

提示

There are three farms (numbered 1..3); farm 1 is a hub. There is a $10 flight from farm 3 to farm 1, and so on. We wish to look for trips from farm 3 to farm 2, from 2->3, and from 1->2.

The trip from 3->2 has only one possible route, of cost 10+7. The trip from 2->3 has no valid route, since there is no flight leaving farm 2. The trip from 1->2 has only one valid route again, of cost 7.