Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$, and a sequence $B$ of length $N$ initially with $B_i = 0$. Write a program to execute the following queries:

• 1 L R X: For all $L \le i \le R$, set $A_i = A_i + X$.
• 2 L R Y: For all $L \le i \le R$, set $A_i = \max(A_i, Y)$.
• 3 L R Y: For all $L \le i \le R$, set $A_i = \min(A_i, Y)$.
• 4 L R: Output $B_L + B_{L+1} + \ldots + B_R$.

Whenever a query of type 1, 2, or 3 causes $A_i$ to change, the value of $B_i$ is increased by $1$.

Input

The first line contains the sequence size $N$. ($1 \le N \le 500{,}000$)

The second line contains $A_1, A_2, \ldots, A_N$. ($-10^9 \le A_i \le 10^9$)

The third line contains the number of queries $M$. ($1 \le M \le 500{,}000$)

The next $M$ lines each describe a query. ($1 \le L \le R \le N$, $-2{,}000 \le X \le 2{,}000$, $-10^9 \le Y \le 10^9$) There is at least one query of type 4.

Output

For each query of type 4, output a single line with the result.

Examples

Input 1

5
1 2 3 4 5
11
4 1 5
1 1 3 3
4 1 5
2 2 5 5
4 1 5
3 1 4 5
4 1 4
2 1 5 0
4 1 5
3 1 5 1
4 1 2

Output 1

0
3
4
5
5
4