SPOJ Brasil

You are given sequence A[0], A[1]...A[N - 1]. (0 ≤ A[i] < 2³²)

You are to perform Q operations:

1. I pos val, insert number val in sequence before element with index pos. (0 ≤ val < 2³², if pos = current_length then you should add number to the end of the sequence)
2. D pos, delete element with index pos from sequence.
3. R pos val, replace element with idex pos by val. (0 ≤ val < 2³²)
4. Q l r k, answer Σ A[i] * (i - l + 1)^k modulo 2³², for l ≤ i ≤ r. (0 ≤ k ≤ 10)

Input

The first line of the input contains an integer N (1 ≤ N ≤ 100000).

The following line contains N integers, representing the starting sequence A[0]...A[N-1].

The third line contains an integer Q (0 ≤ Q ≤ 100000).

Next Q lines contains the queries in given format.

Output

For each "Q" operation, print an integer (one per line) as described above.

Example

Input:
4
1 2 3 5
7
Q 0 2 0
I 3 4
Q 2 4 1
D 0
Q 0 3 1
R 1 2
Q 0 1 0

Output:
6
26
40
4