C. Pekora and Trampolinetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere is a trampoline park with n trampolines in a line. The i-th of which has strength S_i.Pekora can jump on trampolines in multiple passes. She starts the pass by jumping on any trampoline of her choice. If at the moment Pekora jumps on trampoline i, the trampoline will launch her to position i + S_i, and S_i will become equal to \max(S_i-1,1). In other words, S_i will decrease by 1, except of the case S_i=1, when S_i will remain equal to 1. If there is no trampoline in position i + S_i, then this pass is over. Otherwise, Pekora will continue the pass by jumping from the trampoline at position i + S_i by the same rule as above.Pekora can't stop jumping during the pass until she lands at the position larger than n (in which there is no trampoline). Poor Pekora!Pekora is a naughty rabbit and wants to ruin the trampoline park by reducing all S_i to 1. What is the minimum number of passes she needs to reduce all S_i to 1?InputThe first line contains a single integer t (1 \le t \le 500) — the number of test cases.The first line of each test case contains a single integer n (1 \leq n \leq 5000) — the number of trampolines.The second line of each test case contains n integers S_1, S_2, \dots, S_n (1 \le S_i \le 10^9), where S_i is the strength of the i-th trampoline.It's guaranteed that the sum of n over all test cases doesn't exceed 5000.OutputFor each test case, output a single integer — the minimum number of passes Pekora needs to do to reduce all S_i to 1.ExampleInput
3
7
1 4 2 2 2 2 2
2
2 3
5
1 1 1 1 1
Output
4
3
0
NoteFor the first test case, here is an optimal series of passes Pekora can take. (The bolded numbers are the positions that Pekora jumps into during these passes.)  [1,4,\textbf{2},2,\textbf{2},2,\textbf{2}]  [1,\textbf{4},1,2,1,\textbf{2},1]  [1,\textbf{3},1,2,\textbf{1},\textbf{1},\textbf{1}]  [1,\textbf{2},1,\textbf{2},1,\textbf{1},\textbf{1}] For the second test case, the optimal series of passes is show below.  [\textbf{2},3]  [1,\textbf{3}]  [1,\textbf{2}] For the third test case, all S_i are already equal to 1.
3
7
1 4 2 2 2 2 2
2
2 3
5
1 1 1 1 1

4 3 0 
['brute force', 'data structures', 'dp', 'greedy', 'implementation', '*1700']