CF1705B.Mark the Dust Sweeper

Mark is cleaning a row of $n$ rooms. The $i$ -th room has a nonnegative dust level $a_i$ . He has a magical cleaning machine that can do the following three-step operation.

• Select two indices $i<j$ such that the dust levels $a_i$ , $a_{i+1}$ , $\dots$ , $a_{j-1}$ are all strictly greater than $0$ .
• Set $a_i$ to $a_i-1$ .
• Set $a_j$ to $a_j+1$ .

Mark's goal is to make $a_1 = a_2 = \ldots = a_{n-1} = 0$ so that he can nicely sweep the $n$ -th room. Determine the minimum number of operations needed to reach his goal.

The first line contains a single integer $t$ ( $1\leq t\leq 10^4$ ) — the number of test cases.

The first line of each test case contains a single integer $n$ ( $2\leq n\leq 2\cdot 10^5$ ) — the number of rooms.

The second line of each test case contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $0\leq a_i\leq 10^9$ ) — the dust level of each room.

It is guaranteed that the sum of $n$ across all test cases does not exceed $2\cdot 10^5$ .

For each test case, print a line containing a single integer — the minimum number of operations. It can be proven that there is a sequence of operations that meets the goal.

In the first case, one possible sequence of operations is as follows.

• Choose $i=1$ and $j=2$ , yielding the array $[1,1,0]$ .
• Choose $i=1$ and $j=3$ , yielding the array $[0,1,1]$ .
• Choose $i=2$ and $j=3$ , yielding the array $[0,0,2]$ .

At this point, $a_1=a_2=0$ , completing the process.In the second case, one possible sequence of operations is as follows.

• Choose $i=4$ and $j=5$ , yielding the array $[0,2,0,1,1]$ .
• Choose $i=2$ and $j=3$ , yielding the array $[0,1,1,1,1]$ .
• Choose $i=2$ and $j=5$ , yielding the array $[0,0,1,1,2]$ .
• Choose $i=3$ and $j=5$ , yielding the array $[0,0,0,1,3]$ .
• Choose $i=4$ and $j=5$ , yielding the array $[0,0,0,0,4]$ .

In the last case, the array already satisfies the condition.