Hanbyeol's perfect sequence and query class

Hanbyeol's sequence and query class is always known for its perfect lectures. But Hanbyeol is a fool, so even when given a sequence and query problem, he cannot write a program himself and hands the job to you every time. Solve the problem below in his place!

Given a sequence $A_1, A_2, \cdots A_N$ of length $N$, write a program that processes the following queries.

• $1$ $L$ $R$ $X$: For every $L \leq i \leq R$, apply $A_i = \min(A_i, X)$.
• $2$ $L$ $R$ $X$: For every $L \leq i \leq R$, apply $A_i = \max(A_i, X)$.
• $3$ $L$ $R$ $X$: For every $L \leq i \leq R$, apply $A_i = A_i + X$.
• $4$ $L$ $R$: Print $\min(A_L, A_{L+1}, \cdots, A_R)$.
• $5$ $L$ $R$: Print $\max(A_L, A_{L+1}, \cdots, A_R)$.
• $6$ $L$ $R$: Print $A_L + A_{L+1} + \cdots + A_R$.

Note that the range of $X$ is not typical.

The first line contains the size of the sequence $N$. ($1 \leq N \leq 500\,000$)

The second line contains the integers $A_1, A_2, \cdots, A_N$, separated by spaces. ($1 \leq A_i \leq 10^{9}$)

The third line contains the number of queries $M$. ($1 \leq M \leq 300\,000$)

Each of the next $M$ lines contains one query. $X$ is an integer. ($1 \leq L \leq R \leq N$, $1 \leq X \leq \mathbf{10}$)

Print the results of queries 4, 5, and 6, one per line.

The statement of this problem may differ from Hanbyeol's original setting.