Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Playlist

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputManao's friends often send him new songs. He never listens to them right away. Instead, he compiles them into a playlist. When he feels that his mind is open to new music, he opens the playlist and starts to listen to the songs.

Of course, there are some songs that Manao doesn't particuarly enjoy. To get more pleasure from the received songs, he invented the following procedure of listening to the playlist:

- If after listening to some song Manao realizes that he liked it, then he remembers it and starts to listen to the next unlistened song.
- If after listening to some song Manao realizes that he did not like it, he listens to all the songs he liked up to this point and then begins to listen to the next unlistened song.

For example, if Manao has four songs in the playlist, A, B, C, D (in the corresponding order) and he is going to like songs A and C in the end, then the order of listening is the following:

- Manao listens to A, he likes it, he remembers it.
- Manao listens to B, he does not like it, so he listens to A, again.
- Manao listens to C, he likes the song and he remembers it, too.
- Manao listens to D, but does not enjoy it and re-listens to songs A and C.

That is, in the end Manao listens to song A three times, to song C twice and songs B and D once. Note that if Manao once liked a song, he will never dislike it on a subsequent listening.

Manao has received *n* songs: the *i*-th of them is *l*_{i} seconds long and Manao may like it with a probability of *p*_{i} percents. The songs could get on Manao's playlist in any order, so Manao wants to know the maximum expected value of the number of seconds after which the listening process will be over, for all possible permutations of the songs in the playlist.

Input

The first line contains a single integer *n* (1 ≤ *n* ≤ 50000). The *i*-th of the following *n* lines contains two integers, separated by a single space — *l*_{i} and *p*_{i} (15 ≤ *l*_{i} ≤ 1000, 0 ≤ *p*_{i} ≤ 100) — the length of the *i*-th song in seconds and the probability that Manao will like the song, in percents.

Output

In a single line print a single real number — the maximum expected listening time over all permutations of songs. The answer will be considered valid if the absolute or relative error does not exceed 10^{ - 9}.

Examples

Input

3

150 20

150 50

100 50

Output

537.500000000

Input

4

300 0

300 50

240 50

360 80

Output

2121.000000000

Note

Consider the first test case. If Manao listens to the songs in the order in which they were originally compiled, the mathematical expectation will be equal to 467.5 seconds. The maximum expected value is obtained by putting the first song at the end of the playlist.

Consider the second test case. The song which is 360 seconds long should be listened to first. The song 300 seconds long which Manao will dislike for sure should be put in the end.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/23/2017 09:18:54 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|