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F. Fafa and Array
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Fafa has an array A of n positive integers, the function f(A) is defined as . He wants to do q queries of two types:

  • 1 lrx — 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 lrx — 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, ..., an (0 < ai ≤ 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 tilirixi .

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.

Examples
Input
5
1 1 1 1 1
5
1 2 4 1
2 2 3 1
2 4 4 2
2 3 4 1
1 3 3 2
Output
2
8
Input
5
1 2 3 4 5
4
1 2 4 2
2 2 4 1
2 3 4 1
1 2 4 2
Output
6
10