Problem Description
Rar the Cat has an array of N integers. Initially, the ith integer has the value Ai.
Rar the Cat wants you to answer queries and updates, there will be a total of M queries and updates, in order.
For each query, Rar the Cat will provide you with two integers x and y where 0 < x ≤ y ≤ N. You are to respond with the sum of the integers from A[x] to A[y] inclusive.
For each update, Rar the Cat 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) ≤ Ai, 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 sum 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
3
41
97
34