A13576. Omkar and Password

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?

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 $2 \cdot 10^5$ .

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

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.