牛客网暑期ACM多校训练营（第三场）H Diff-prime Pairs (贡献)

链接：https://ac.nowcoder.com/acm/contest/141/H来源：牛客网

Eddy has solved lots of problem involving calculating the number of coprime pairs within some range. This problem can be solved with inclusion-exclusion method. Eddy has implemented it lots of times. Someday, when he encounters another coprime pairs problem, he comes up with diff-prime pairs problem. diff-prime pairs problem is that given N, you need to find the number of pairs (i, j), where igcd(i,j)\frac{i}{gcd(i, j)}gcd(i,j)i and jgcd(i,j)\frac{j}{gcd(i,j)}gcd(i,j)j are both prime and i ,j ≤ N. gcd(i, j) is the greatest common divisor of i and j. Prime is an integer greater than 1 and has only 2 positive divisors.

Eddy tried to solve it with inclusion-exclusion method but failed. Please help Eddy to solve this problem.

Note that pair (i1, j1) and pair (i2, j2) are considered different if i1 ≠ i2 or j1 ≠ j2.

输入描述:

Input has only one line containing a positive integer N.1 ≤ N ≤ 107

输出描述:

Output one line containing a non-negative integer indicating the number of diff-prime pairs (i,j) where i, j ≤ N

示例1

输入

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巴特西

牛客网暑期ACM多校训练营（第三场）H Diff-prime Pairs (贡献)