Twin Prime Pairs

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Count pairs (p,p+2) of primes where both elements lie in the inclusive interval [l,r], counted once by smaller member.

Input

Two integers l r.

Output

Number of twin prime pairs.

Subtasks

• Subtask 1 (20%): 1 ≤ l ≤ r ≤ 100.

• Subtask 2 (30%): 1 ≤ l ≤ r ≤ 2000.

• Subtask 3 (50%): 1 ≤ l ≤ r ≤ 20000.

Examples

Example 1

Input:

2 13

Output:

3

Explanation: The three pairs are (3,5), (5,7), and (11,13).

Example 2

Input:

11 12

Output:

0

Explanation: Thirteen falls outside the interval.