Range Max Query

Problem Description

Coco the Monkey has an array of N integers. Initially, the i^th integer has the value A_i.

Coco the Monkey wants you to answer queries and updates, there will be a total of M queries and updates, in order.

For each query, Coco the Monkey will provide you with two integers x and y where 0 ≤ x ≤ y ≤ N. You are to respond with the maximum value of the integers from A[x] to A[y] inclusive.

For each update, Coco the Monkey will provide you with three integers, a, b and c. This means you have to add c to every integer from A[a] to A[b].

Limits

For all testcases, -(10³) ≤ A_i, c ≤ 10³, 0 ≤ x ≤ y < N, 0 ≤ a ≤ b < N.

Subtask 1 (57%): 1 ≤ N ≤ 100000, 0 ≤ M ≤ 200000. For all update commands, a = b.

Subtask 2 (43%): 1 ≤ N ≤ 100000, 0 ≤ M ≤ 200000. No further restrictions.

Subtask 3 (0%): Sample Testcases.

Input

The first line of input will contain one integer, N.

The second line of input will contain N integers, representing the array A.

The next line will contain a single integer, M.

M lines will follow. The first character of each line will be T.

If T is 0, then it represents a query. 2 integers will then follow, x and y.

If T is 1, then it represents a update. 3 integers will then follow, a, b followed by c.

Output

For each line of query, you are to output the maximum value of A[x] to A[y] inclusive, on a single line.

Sample Testcase 1

Input

10
1 2 9 5 7 6 3 4 2 2
5
0 0 1
0 0 9
1 1 8 7
0 0 9
0 5 7

Output

2
9
16
13