Fafa has an array A of n positive integers, the function f(A) is defined as $\text{[math]}$ . He wants to do q queries of two types:

1 l r x — find the maximum possible value of f(A), if x is to be added to one element in the range [l, r]. You can choose to which element to add x.
2 l r x — increase all the elements in the range [l, r] by value x.

Note that queries of type 1 don't affect the array elements.

Input

The first line contains one integer n (3 ≤ n ≤ 10⁵) — the length of the array.

The second line contains n positive integers a₁, a₂, ..., a_n (0 < a_i ≤ 10⁹) — the array elements.

The third line contains an integer q (1 ≤ q ≤ 10⁵) — the number of queries.

Then q lines follow, line i describes the i-th query and contains four integers t_i l_i r_i x_i $\text{[math]}$ .

It is guaranteed that at least one of the queries is of type 1.

Output

For each query of type 1, print the answer to the query.

Fafa and Array