# Graph Labelling SOLUTIONS GPHLBL

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### Graph Labelling SOLUTIONS GPHLBL

You are given a coordinated chart G with N vertices (numbered 1 through N) and M edges. We should signify the arrangement of its vertices by V, the arrangement of its edges by E and an edge from a vertex u to a vertex v by (u,v). At that point, how about we characterize:

For each u,v∈V, R(u,v) is valid if v can be reached from u or bogus in any case. In particular, if u=v, it is in every case valid.

For each v∈V, a lot of vertices N(v)={u∈V∣R(u,v)∧R(v,u)}.

For every subset U⊆V, two arrangements of edges Out(U)={(u,v)∈E∣u∈U} and In(U)={(v,u)∈E∣u∈U}.

You have to allocate a mark to each edge in E; you may just utilize names 1 and 2. The expenses of marking an edge are c1 and c2 for the names 1 and 2 separately.

In the subsequent chart, Q limitations (numbered 1 through Q) should be fulfilled. For each substantial I, the I-th limitation is that the quantity of edges in a set Si with the name xi ought to be among li and ri (comprehensive); Si is controlled by a given vertex wi and the kind of this imperative ti as follows:

ti=1: Si=Out(N(wi))

ti=2: Si=In(N(wi))

ti=3: Si=Out({wi})

ti=4: Si=In({wi})

Locate the littlest expense of naming all the edges so that these Q requirements are fulfilled or establish that there is no arrangement fulfilling all limitations.

Info

The main line of the info contains a solitary whole number T meaning the quantity of experiments. The portrayal of T experiments follows.

The main line of each experiment contains three space-isolated whole numbers N, M and Q.

Every one of the accompanying M lines contains two space-isolated whole numbers u and v meaning a coordinated edge (u,v).

The following line contains two space-isolated whole numbers c1 and c2.

Q lines follow. For each legitimate I, the I-th of these lines contains five space-isolated numbers ti, wi, xi, li and ri.

Yield

For each experiment, print a solitary line containing one whole number ― the littlest expense of marking the edges or −1 in the event that it is difficult to name the edges so that all requirements are fulfilled.

Imperatives

1≤T≤100

1≤N≤3⋅104

0≤M≤3⋅104

0≤Q≤3⋅105

1≤u,v≤N

1≤c1,c2≤109

1≤ti≤4 for each substantial I

1≤wi≤N for each legitimate I

xi∈{1,2} for each legitimate I

0≤li≤ri≤M for each legitimate I

the whole of N over all experiments doesn’t surpass 6⋅104

the whole of M over all experiments doesn’t surpass 6⋅104

the whole of Q over all experiments doesn’t surpass 6⋅105

Model Input

4 1

1 2

2 3

1 3

3 4

10 20

3 1

Model Output

50

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