Omkar and Password

2000ms

262144K

Description:

Lord Omkar has permitted you to enter the Holy Church of Omkar! To test your worthiness, Omkar gives you a password which you must interpret!

A password is an array $$$a$$$ of $$$n$$$ positive integers. You apply the following operation to the array: pick any two adjacent numbers that are not equal to each other and replace them with their sum. Formally, choose an index $$$i$$$ such that $$$1 \leq i < n$$$ and $$$a_{i} \neq a_{i+1}$$$, delete both $$$a_i$$$ and $$$a_{i+1}$$$ from the array and put $$$a_{i}+a_{i+1}$$$ in their place.

For example, for array $$$[7, 4, 3, 7]$$$ you can choose $$$i = 2$$$ and the array will become $$$[7, 4+3, 7] = [7, 7, 7]$$$. Note that in this array you can't apply this operation anymore.

Notice that one operation will decrease the size of the password by $$$1$$$. What is the shortest possible length of the password after some number (possibly $$$0$$$) of operations?

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). Description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the length of the password.

The second line of each test case contains $$$n$$$ integers $$$a_{1},a_{2},\dots,a_{n}$$$ ($$$1 \leq a_{i} \leq 10^9$$$) — the initial contents of your password.

The sum of $$$n$$$ over all test cases will not exceed $$$2 \cdot 10^5$$$.

Output:

For each password, print one integer: the shortest possible length of the password after some number of operations.

Sample Input:

Sample Output:

1
2

Note:

In the first test case, you can do the following to achieve a length of $$$1$$$:

Pick $$$i=2$$$ to get $$$[2, 4, 1]$$$

Pick $$$i=1$$$ to get $$$[6, 1]$$$

Pick $$$i=1$$$ to get $$$[7]$$$

In the second test case, you can't perform any operations because there is no valid $$$i$$$ that satisfies the requirements mentioned above.

Informação

Provedor Codeforces

Código CF1392A