CF1462D.Add to Neighbour and Remove

Polycarp was given an array of $a[1 \dots n]$ of $n$ integers. He can perform the following operation with the array $a$ no more than $n$ times:

• Polycarp selects the index $i$ and adds the value $a_i$ to one of his choice of its neighbors. More formally, Polycarp adds the value of $a_i$ to $a_{i-1}$ or to $a_{i+1}$ (if such a neighbor does not exist, then it is impossible to add to it).
• After adding it, Polycarp removes the $i$ -th element from the $a$ array. During this step the length of $a$ is decreased by $1$ .

The two items above together denote one single operation.

For example, if Polycarp has an array $a = [3, 1, 6, 6, 2]$ , then it can perform the following sequence of operations with it:

• Polycarp selects $i = 2$ and adds the value $a_i$ to $(i-1)$ -th element: $a = [4, 6, 6, 2]$ .
• Polycarp selects $i = 1$ and adds the value $a_i$ to $(i+1)$ -th element: $a = [10, 6, 2]$ .
• Polycarp selects $i = 3$ and adds the value $a_i$ to $(i-1)$ -th element: $a = [10, 8]$ .
• Polycarp selects $i = 2$ and adds the value $a_i$ to $(i-1)$ -th element: $a = [18]$ .

Note that Polycarp could stop performing operations at any time.

Polycarp wondered how many minimum operations he would need to perform to make all the elements of $a$ equal (i.e., he wants all $a_i$ are equal to each other).

The first line contains a single integer $t$ ( $1 \leq t \leq 3000$ ) — the number of test cases in the test. Then $t$ test cases follow.

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 3000$ ) — the length of the array. The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^5$ ) — array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $3000$ .

For each test case, output a single number — the minimum number of operations that Polycarp needs to perform so that all elements of the $a$ array are the same (equal).

In the first test case of the example, the answer can be constructed like this (just one way among many other ways):

$[3, 1, 6, 6, 2]$ $\xrightarrow[]{i=4,~add~to~left}$ $[3, 1, 12, 2]$ $\xrightarrow[]{i=2,~add~to~right}$ $[3, 13, 2]$ $\xrightarrow[]{i=1,~add~to~right}$ $[16, 2]$ $\xrightarrow[]{i=2,~add~to~left}$ $[18]$ . All elements of the array $[18]$ are the same.

In the second test case of the example, the answer can be constructed like this (just one way among other ways):

$[1, 2, 2, 1]$ $\xrightarrow[]{i=1,~add~to~right}$ $[3, 2, 1]$ $\xrightarrow[]{i=3,~add~to~left}$ $[3, 3]$ . All elements of the array $[3, 3]$ are the same.

In the third test case of the example, Polycarp doesn't need to perform any operations since $[2, 2, 2]$ contains equal (same) elements only.

In the fourth test case of the example, the answer can be constructed like this (just one way among other ways):

$[6, 3, 2, 1]$ $\xrightarrow[]{i=3,~add~to~right}$ $[6, 3, 3]$ $\xrightarrow[]{i=3,~add~to~left}$ $[6, 6]$ . All elements of the array $[6, 6]$ are the same.