Pekora can hop on trampolines in numerous passes. She begins the pass by hopping on any trampoline of her decision. If right now Pekora bounces on trampoline I, the trampoline will dispatch her to situate i+Si, and Si will become equivalent to max(Si−1,1). As such, Si will diminish by 1, besides of the case Si=1, when Si will stay equivalent to 1.
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Pekora can hop on trampolines in numerous passes. She begins the pass by hopping on any trampoline of her decision.
If right now Pekora bounces on trampoline I, the trampoline will dispatch her to situate i+Si, and Si will become equivalent to max(Si−1,1). As such, Si will diminish by 1, besides of the case Si=1, when Si will stay equivalent to 1.
In the event that there is no trampoline in position i+Si, this ignore is. Any other way, Pekora will proceed with the pass by bouncing from the trampoline at position i+Si by a similar guideline as above.
Pekora can't quit hopping during the pass until she arrives at the position bigger than n (in which there is no trampoline). Poor Pekora!
Pekora is a devious bunny and needs to demolish the jumping center by decreasing all Si to 1. What is the base number of passes she wants to decrease all Si to 1?
Input
The main line contains a solitary integer t (1≤t≤500) — the number of experiments.
The principal line of each experiment contains a solitary integer n (1≤n≤5000) — the number of trampolines.
The second line of each experiment contains n integers S1,S2,… ,Sn (1≤Si≤109), where Si is the strength of the I-th trampoline.
It's surefire that the amount of n over all experiments doesn't surpass 5000.
Output
For each experiment, output a solitary integer — the base number of passes Pekora needs to do to lessen all Si to 1.
Step by step
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