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C. Subset Sums

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an array *a*_{1}, *a*_{2}, ..., *a*_{n} and *m* sets *S*_{1}, *S*_{2}, ..., *S*_{m} of indices of elements of this array. Let's denote *S*_{k} = {*S*_{k, i}} (1 ≤ *i* ≤ |*S*_{k}|). In other words, *S*_{k, i} is some element from set *S*_{k}.

In this problem you have to answer *q* queries of the two types:

- Find the sum of elements with indices from set
*S*_{k}: . The query format is "? k". - Add number
*x*to all elements at indices from set*S*_{k}:*a*_{Sk, i}is replaced by*a*_{Sk, i}+*x*for all*i*(1 ≤*i*≤ |*S*_{k}|). The query format is "+ k x".

After each first type query print the required sum.

Input

The first line contains integers *n*, *m*, *q* (1 ≤ *n*, *m*, *q* ≤ 10^{5}). The second line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (|*a*_{i}| ≤ 10^{8}) — elements of array *a*.

Each of the following *m* lines describes one set of indices. The *k*-th line first contains a positive integer, representing the number of elements in set (|*S*_{k}|), then follow |*S*_{k}| distinct integers *S*_{k, 1}, *S*_{k, 2}, ..., *S*_{k, |Sk|} (1 ≤ *S*_{k, i} ≤ *n*) — elements of set *S*_{k}.

The next *q* lines contain queries. Each query looks like either "? k" or "+ k x" and sits on a single line. For all queries the following limits are held: 1 ≤ *k* ≤ *m*, |*x*| ≤ 10^{8}. The queries are given in order they need to be answered.

It is guaranteed that the sum of sizes of all sets *S*_{k} doesn't exceed 10^{5}.

Output

After each first type query print the required sum on a single line.

Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

5 3 5

5 -5 5 1 -4

2 1 2

4 2 1 4 5

2 2 5

? 2

+ 3 4

? 1

+ 2 1

? 2

Output

-3

4

9

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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