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Leonardo loves primes and created queries where each query takes the form of an integer, . For each , he wants you to count the maximum number of unique prime factors of any number in the inclusive range and then print this value on a new line.

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

Input Format

The first line contains an integer, , denoting the number of queries. Each line of the subsequent lines contains a single integer, .

Constraints

Output Format

For each query, print the maximum number of unique prime factors for any number in the inclusive range on a new line.

Sample Input

6 1 2 3 500 5000 10000000000

Sample Output

0 1 1 4 5 10

Explanation

The maximum number of unique prime factors of any number in the inclusive range is , because is not prime and its only factor is itself.

The maximum number of unique prime factors of any number in the inclusive range is . We already know that the number has prime factors, but has prime factor (itself).

The maximum number of unique prime factors of any number in the inclusive range is . The number has prime factor (itself), and we already know that the number has prime factor and the number has prime factors.

The maximum number of unique prime factors in the inclusive range is . The product of our first four unique primes is , and there are no additional unique primes we can multiply that number by that results in a value .