Ruins is driving a car to participating in a programming contest. As on a very tight schedule, he will drive the car without any slow down, so the speed of the car is non-decrease real number.

Of course, his speeding caught the attention of the traffic police. Police record $N$ positions of Ruins without time mark, the only thing they know is every position is recorded at an integer time point and Ruins started at $0$.

Now they want to know the**minimum** time that Ruins used to pass the last position.

Of course, his speeding caught the attention of the traffic police. Police record $N$ positions of Ruins without time mark, the only thing they know is every position is recorded at an integer time point and Ruins started at $0$.

Now they want to know the

First line contains an integer $T$, which indicates the number of test cases.

Every test case begins with an integers $N$, which is the number of the recorded positions.

The second line contains $N$ numbers $a_1$, $a_2$, $\cdots$, $a_N$, indicating the recorded positions.

Limits

$1 \leq T \leq 100$

$1 \leq N \leq 10^5$

$0 < ai \leq 10^9$

$a_i < a_{i+1}$

Every test case begins with an integers $N$, which is the number of the recorded positions.

The second line contains $N$ numbers $a_1$, $a_2$, $\cdots$, $a_N$, indicating the recorded positions.

Limits

$1 \leq T \leq 100$

$1 \leq N \leq 10^5$

$0 < ai \leq 10^9$

$a_i < a_{i+1}$

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