The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 202 (Div. 1) |
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Finished |

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brute force

data structures

*2500

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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 2010-2024 Mike Mirzayanov

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