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Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible optimal list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible optimal list of factors is: (1, 17, 59, 127).

Related to this old question.

Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible list of factors is: (1, 17, 59, 127).

Related to this old question.

Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible optimal list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible optimal list of factors is: (1, 17, 59, 127).

Related to this old question.

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Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible list of factors is: (1, 17, 59, 127).

Related to this old question.

Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible list of factors is: (1, 17, 59, 127).

Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible list of factors is: (1, 17, 59, 127).

Related to this old question.

1
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A factorization game

Input

A single integer \$1 \leq x \leq 10^{15}\$.

Output

The maximum number of distinct positive integers that have the product \$x\$.

Examples

Input: 1099511627776. Output: 9. One possible list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible list of factors is: (1, 17, 59, 127).