You are given a sequence $A_1, A_2, \ldots, A_N$ of length $N$. Write a program to process the following queries:

• 1 L R X: For every $i$ such that $L \le i \le R$, set $A_i = A_i + X$.
• 2 L R: For every $i$ such that $L \le i \le R$, set $A_i = \lfloor \sqrt{A_i} \rfloor$.
• 3 L R: Output $A_L + A_{L+1} + \ldots + A_R$.

Input

The first line contains the size of the sequence $N$. ($1 \le N \le 100{,}000$)

The second line contains $A_1, A_2, \ldots, A_N$. ($1 \le A_i \le 100{,}000$)

The third line contains the number of queries $M$. ($1 \le M \le 100{,}000$)

The next $M$ lines each contain a query. ($1 \le L \le R \le N$, $1 \le X \le 100{,}000$) At least one type-3 query appears.

Output

Output the results of each type-3 query in order, one per line.

Examples

Input 1

5
1 2 3 4 5
5
1 3 5 2
2 1 4
3 2 4
2 3 5
3 1 5

Output 1

5
6