Divisibility Count in Concatenated Number Sequence

A mysterious creature challenges you with a mathematical puzzle. The creature has written a sequence of numbers on the ground which are formed by concatenating the natural numbers incrementally:

\(1,\; 12,\; 123,\; 1234,\; 12345,\; \dots,\; 12345678910,\; \dots,\; 1234567891011,\; \dots\)

The k^th term in the sequence is the number formed by concatenating together the numbers 1, 2, 3, ..., k. The creature then challenges: "If you can compute how many of the first \(n\) terms of this sequence are divisible by \(3\), I will let you pass. Otherwise... well, I might have to eat you!"

Your task is to help solve this puzzle. Note that a number is divisible by \(3\) if and only if the sum of its digits is divisible by \(3\). For the k^th term, the sum of its digits is equal to \(\sum_{i=1}^{k} s(i)\), where \(s(i)\) is the sum of the digits of \(i\). Since for any positive integer \(i\), we have \(s(i) \equiv i \pmod{3}\), the digit sum modulo \(3\) is equivalent to the sum \(1+2+\cdots+k = \frac{k(k+1)}{2}\).

Thus the problem reduces to counting the number of integers \(k\) (with \(1 \le k \le n\)) such that

\(\frac{k(k+1)}{2} \equiv 0 \pmod{3}\).

It can be proven that this congruence holds if and only if \(k \equiv 0\) or \(k \equiv 2 \pmod{3}\). Your program should compute the total count of such \(k\) values.

inputFormat

The input consists of a single integer \(n\) representing the number of terms to consider in the sequence.

outputFormat

Output a single integer indicating how many of the first \(n\) terms of the sequence are divisible by \(3\).

sample

6

4