### Product

Time Limit: 4000/2000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

#### Problem Description

For set $$A$$, let $v(A) = \sum_{S \subset A, |S| \equiv 1 \pmod 2}(\prod_{x \in S}x)$

Initially, $$A$$ is empty. Your task is to insert and delete element keeping track of value of $$v(A)$$.

#### Input

The first line contains the only integer $$q$$, which denotes the number of operations.

The following $$q$$ lines, which is either "insert $$x$$" or "delete $$x$$".

For convinience, one can assume that $$A$$ is a multiset and there are no delete operations for non-exist elements.

$$(1 \leq q \leq 10^5, 2 \leq x \leq 10^9)$$

#### Output

After each operation, print a single integer showing $$v(A) \bmod (10^9 + 7)$$.

#### Sample Input

4
insert 2
insert 3
insert 4
delete 3

#### Sample Output

2
5
33
6

#### Hint

After $$4$$ is inserted, $$A = \{2, 3, 4\}$$. Thus, $$v(A) = 2 + 3 + 4 + 2 \cdot 3 \cdot 4 = 33$$.

ftiasch

#### Manager

Information
 Solved Number 18 Submit Number 95
Problem Tags
number theory
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