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## [Solution] Strong Elements CodeChef Solution

Chef has an array $A$ of length $N$.

An index $i$ is called strong if we can change the gcd of the whole array just by changing the value of ${A}_{i}$.

Determine the number of strong indices in the array.

### Input Format

• First line will contain $T$, number of test cases. Then the test cases follow.
• First line of each test case contains an integer $N$ denoting the size of the array $A$.

• Second line contains $N$ space separated integers ${A}_{1},{A}_{2},\dots ,{A}_{N}$ - denoting the array $A$.

### Output Format

For each test case, output the number of strong indices in the array.

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### Constraints

• $1\le T\le 5\cdot {10}^{4}$
• $2\le N\le 3\cdot {10}^{5}$