Mark the Dust Sweeper

1000ms

262144K

Description:

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.

Input:

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 $$$2\cdot 10^5$$$.

Output:

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.

Sample Input:

4
3
2 0 0
5
0 2 0 2 0
6
2 0 3 0 4 6
4
0 0 0 10

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1705B