Add to Neighbour and Remove

3000ms

262144K

Description:

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).

Input:

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 $$$3000$$$.

Output:

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).

Sample Input:

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1462D