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- Prepare
- Mathematics
- Fundamentals
- Leonardo's Prime Factors

# Leonardo's Prime Factors

# Leonardo's Prime Factors

Leonardo loves primes and created queries where each query takes the form of an integer, . For each , count the maximum number of distinct prime factors of any number in the inclusive range .

**Note:** Recall that a prime number is only divisible by and itself, and is *not* a prime number.

**Example**

The maximum number of distinct prime factors for values less than or equal to is . One value with distinct prime factors is . Another is .

**Function Description**

Complete the *primeCount* function in the editor below.

*primeCount* has the following parameters:

*int n:*the inclusive limit of the range to check

**Returns**

*int:*the maximum number of distinct prime factors of any number in the inclusive range .

**Input Format**

The first line contains an integer, , the number of queries.

Each of the next lines contains a single integer, .

**Constraints**

**Sample Input**

```
6
1
2
3
500
5000
10000000000
```

**Sample Output**

```
0
1
1
4
5
10
```

**Explanation**

- is not prime and its only factor is itself.
- has prime factor, .
- The number has prime factor, , has and has prime factors.
- The product of the first four primes is . While higher value primes may be a factor of some numbers, there will never be more than distinct prime factors for a number in this range.