???The Heaviest Non-decreasing Subsequence Problem

Let $S$ be a sequence of integers s_{1}s?1??, s_{2}s?2??, $...$, s_{n}s?n?? Each integer is is associated with a weight by the following rules:

(1) If is is negative, then its weight is $0$.

(2) If is is greater than or equal to $10000$, then its weight is $5$. Furthermore, the real integer value of s_{i}s?i?? is s_{i}-10000s?i???10000 . For example, if s_{i}s?i?? is $10101$, then is is reset to $101$ and its weight is $5$.

(3) Otherwise, its weight is $1$.

A non-decreasing subsequence of $S$ is a subsequence s_{i1}s?i1??, s_{i2}s?i2??, $...$, s_{ik}s?ik??, with i_{1}<i_{2}\ ...\ <i_{k}i?1??<i?2?? ... <i?k??, such that, for all $1\le j<k$, we have s_{ij}<s_{ij+1}s?ij??<s?ij+1??.

A heaviest non-decreasing subsequence of $S$ is a non-decreasing subsequence with the maximum sum of weights.

Write a program that reads a sequence of integers, and outputs the weight of its

heaviest non-decreasing subsequence. For example, given the following sequence:

$80$ $75$ $73$ $93$ $73$ $73$ $10101$ $97$ $?1$ $?1$ $114$ $?1$ $10113$ $118$

The heaviest non-decreasing subsequence of the sequence is $<73,73,73,101,113,118>$ with the total weight being $1+1+1+5+5+1=14$. Therefore, your program should output $14$ in this example.

We guarantee that the length of the sequence does not exceed 2*10^{5}2?10?5??

Input Format

A list of integers separated by blanks:s_{1}s?1??, s_{2}s?2??,$...$,s_{n}s?n??

Output Format

A positive integer that is the weight of the heaviest non-decreasing subsequence.