Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$, and two sequences $B$ and $C$ of length $N$, initially satisfying $B_i = A_i$ and $C_i = A_i$. Write a program to process 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 $\min(A_L, A_{L+1}, \ldots, A_R)$.
• 5 L R: Output $\min(B_L, B_{L+1}, \ldots, B_R)$.
• 6 L R: Output $\max(C_L, C_{L+1}, \ldots, C_R)$.

After each query, for all $1 \le i \le N$, update $B_i = \min(B_i, A_i)$ and $C_i = \max(C_i, A_i)$.

Input

The first line contains an integer $N$, the length of the sequence. ($1 \le N \le 500{,}000$)

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

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

The next $M$ lines each contain a query. ($1 \le L \le R \le N$, $-2{,}000 \le X \le 2{,}000$, $-10^9 \le Y \le 10^9$) Queries of types $4$, $5$, and $6$ each appear at least once.

Output

For each query of types $4$, $5$, and $6$, output the answer, each on a separate line.

Examples

Input 1

3
1 2 3
6
5 3 3
1 2 3 -2
3 1 3 0
5 3 3
2 2 3 4
5 1 3

Output 1

3
0
0