Description

Find the number of ordered positive integer solutions to the equation:

Output the answer modulo $10^9+7$.

Input Format

The input consists of a single integer $n$.

Output Format

Output a single integer: the number of ordered positive integer pairs $(x, y)$ modulo $10^9+7$.

2

3

1439

102426508

Hint

Sample 1 Explanation

There are three pairs $(x, y)$ that satisfy the condition: $(3,6)$, $(4,4)$, and $(6,3)$.

Constraints

• For $30\%$ of the testdata, it is guaranteed that $n \le 100$.
• For $100\%$ of the testdata, it is guaranteed that $1 \le n \le 10^6$.

Translated by ChatGPT 5