The I-th stage is named with an integer artificial intelligence (0≤ai≤n−i). At the point when the character is remaining on the I-th stage, the player can move the character to any of the j-th stages where i+1≤j≤i+ai. If the character is on the I-th stage where ai=0 and i≠n, the player loses the game. Since Gildong thinks the current game isn't adequately hard, he needs to make it
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The I-th stage is named with an integer
Since Gildong thinks the current game isn't adequately hard, he needs to make it considerably harder. He needs to change a few (perhaps zero) names to 0 so that there remains precisely one way of winning. He needs to alter the game as little as could really be expected, so he's requesting you to see as the base number from stages that ought to have their names changed. Two different ways are unique if and provided that there exists a stage the character gets to in one manner however not in the alternate manner.
Input
Each test contains at least one experiments. The main line contains the number of experiments t (1≤t≤500).
Each experiment contains two lines. The main line of each experiment comprises of an integer n (2≤n≤3000) — the number of foundation of the game.
The second line of each experiment contains n integers. The I-th integer is computer based intelligence (0≤ai≤n−i) — the integer of the I-th stage.
It is ensured that:
For each experiment, there is something like one way of winning at first.
The amount of n in all experiments doesn't surpass 3000.
Output
For each experiment, print one integer — the base number of various marks that ought to be changed to 0 so that there remains precisely one way of winning.
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