Problem Statement

You are initially given an array of N integers ( 1<=N<=10⁵ ). Given this array, you have to perform 2 kinds of operations :

(i) Operation 1 : Op1( l, r )

You are given 2 integers l and r. ( 1 <= l <= r <= current size of the array ). You need to return the sum of all the elements with indices between l and r ( both inclusive ). That is, if the elements currently in the array are a₁, a₂, a₃.... a_n, you need to return the following sum : a_l + a_l+1 + a_l+2 ... + a_r.

(ii) Operation 2 : Op2( x )

You are given a single integer x ( |x| <= 10⁹ ). Add this element to the beginning of the array. After this operation, x will now become a₁, the old a₁ will now become a₂, and so on. The size of the array will increase by 1.

Input

The first line contains a single integer N ( 1 <= N <= 10⁵ ), the number of elements initially in the array.

This is followed by a line containing N space separated integers, a₁ a₂ .... a_N. ( |a_i| <= 10⁹ )

The next line contains a single integer Q, the number of operations you will be asked to perform. ( 1 <= Q <= 10⁵ )

Q lines of input follow. Each such line starts with either the number 1 or the number 2. This indicates the type of operation that you are required to perform. The format of these queries are as follows :

1 l r : Carry out operation 1 with arguments l and r. ( 1 <= l <= r <= current size of the array )
That is, return the sum of the following array elements : a_l + a_l+1 ... + a_r

2 x : Carry out operation 2 with the argument x. ( |x| <= 10⁹ )
That is, add the value x at the beginning of the array.

Output

For each query of type 1, output the return value on a new line. No output needs to be printed for queries of type 2.

Example

Input #1:
10
1 2 3 4 5 6 7 8 9 10
4
1 1 10
1 1 1
1 10 10
1 2 7

Output #1:
55
1
10
27


Input #2:
5
6 7 8 9 10
9
2 5
2 4
1 2 7
2 3
2 2
2 1
1 1 10
1 1 1
1 10 10


Output #2:
45
55
1
10