You are given an array a₁, a₂, ..., a_n and m sets S₁, S₂, ..., 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: $\text{[math]}$ . The query format is "? k".
Add number x to all elements at indices from set S_k: a_{S_k, i} is replaced by a_{S_k, 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 ≤ 10⁵). The second line contains n integers a₁, a₂, ..., a_n (|a_i| ≤ 10⁸) — 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, |S_k|} (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| ≤ 10⁸. 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 10⁵.

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.

Subset Sums

Examples