CT16E - Fish

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n fish, numbered from 1 to n, live in a lake. Every day right one pair of fish meet, and the probability of each other pair meeting is the same. If two fish with indexes i and j meet, the first will eat up the second with the probability aij, and the second will eat up the first with the probability aji = 1 - aij. The described process goes on until there are at least two fish in the lake. For each fish find out the probability that it will survive to be the last in the lake.

Input

The first line contains integer n (1 ≤ n ≤  18) — the amount of fish in the lake. Then there follow n lines with n real numbers each — matrix a. aij (0 ≤ aij  ≤ 1) — the probability that fish with index i eats up fish with index j. It's guaranteed that the main diagonal contains zeros only, and for other elements the following is true: aij = 1 -  aji. All real numbers are given with not more than 6 characters after the decimal point.

Output

Output n space-separated real numbers accurate to not less than 6 decimal places. Number with index i should be equal to the probability that fish with index i will survive to be the last in the lake.

Example

Input:
5
0 1 1 1 1
0 0 0.5 0.5 0.5
0 0.5 0 0.5 0.5
0 0.5 0.5 0 0.5
0 0.5 0.5 0.5 0

Output:
1.000000 0.000000 0.000000 0.000000 0.000000 

hide comments
iampk: 2018-12-04 17:30:40

Can someone please provide a good test case for the problem?

magick968: 2011-09-24 11:52:26

Time limit is far too strict.

Mahesh Chandra Sharma: 2010-12-08 22:55:26

For the max case of n = 18 my program runs on local machine in just 1.1 sec. still it is giving TLE.
before setting the time limit problem setters should keep in mind that SPOJ servers are slow.

Last edit: 2010-12-09 00:31:35
little zaza: 2010-07-17 02:40:08

TL is a too strict, memoization got TLE

Phan Công Minh: 2010-07-12 04:39:28

n^2* 2^n is enough to pass . if You got tle, you should inprove your code.

Ravi Kiran: 2010-07-11 14:22:30

O(N*N*2^N) is enough to get ac.Maybe evident optimisations are required!
Mine is strictly N*N*2^N during solve process!

Ishan: 2010-07-08 07:45:00

O(n*n*2^n) is getting tle.time limit should be relaxed.

[Rampage] Blue.Mary: 2010-06-26 10:24:17

Maybe 5 second time limit is more proper?

kostya: 2010-06-25 05:12:03

0.9047615 in result must be 0.904761 or 0.904762?

Phan Công Minh: 2010-06-25 01:10:50

2
0 0.5
0.5 0

ans
0.5 0.5

Last edit: 2010-06-25 01:13:32

Added by:Phan Công Minh
Date:2010-06-22
Time limit:0.288s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 SQLITE VB.NET
Resource:Codeforces