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Problems

Power Network

Power Network

Time limit 1 second
Memory limit 64 MiB

A power network consists of nodes (power stations, consumers and dispatchers) connected by power transport lines. A node u may be supplied with an amount s(u)0 of power, may produce an amount 0p(u)p_max(u) of power, may consume an amount 0c(u)min(s(u),c_max(u)) of power, and may deliver an amount d(u)=s(u)+p(u)-c(u) of power. The following restrictions apply: c(u)=0 for any power station, p(u)=0 for any consumer, and p(u)=c(u)=0 for any dispatcher. There is at most one power transport line (u,v) from a node u to a node v in the net; it transports an amount 0l(u,v)l_max(u,v) of power delivered by u to v. Let Con = _u(cu) be the power consumed in the net. The problem is to compute the maximum value of Con.

An example is in figure. The label x/y of power station u shows that p(u)=x and p_max(u)=y. The label x/y of consumer u shows that c(u)=x and c_max(u)=y. The label x/y of power transport line (u,v) shows that l(u,v)=x and l_max(u,v)=y. The power consumed is Con=6. Notice that there are other possible states of the network but the value of Con cannot exceed 6.

Input data

There are several data sets in the input text file. Each data set encodes a power network. It starts with four integers: 0n100 (nodes), 0n_pn (power stations), 0n_cn (consumers), and 0mn^2 (power transport lines). Follow m data triplets (u,v)z, where u and v are node identifiers (starting from 0) and 0z1000 is the value of l_max(u,v). Follow n_p doublets (u)z, where u is the identifier of a power station and 0z10000 is the value of p_max(u). The data set ends with n_c doublets (u)z, where u is the identifier of a consumer and 0z10000 is the value of c_max(u). All input numbers are integers. Except the (u,v)z triplets and the (u)z doublets, which do not contain white spaces, white spaces can occur freely in input. Input data terminate with an end of file and are correct.

Output data

For each data set from the input, the program prints on the standard output the maximum amount of power that can be consumed in the corresponding network. Each result has an integral value and is printed from the beginning of a separate line.

Examples

Input example #1
2 1 1 2 (0,1)20 (1,0)10 (0)15 (1)20
7 2 3 13 (0,0)1 (0,1)2 (0,2)5 (1,0)1 (1,2)8 (2,3)1 (2,4)7 (3,5)2 (3,6)5 (4,2)7 (4,3)5 (4,5)1 (6,0)5 (0)5 (1)2 (3)2 (4)1 (5)4
Output example #1
15
6
Source ACM ICPC Southeastern European Regional Programming Contest, Bucharest, Romania, October 18, 2003