Limits
5s, 512 MB

This problem is very easy. There's a graph of `$N$`

nodes. Each edge `$u-v$`

(`$u >= v ; u = v$`

is possible, i.e. a loop) has some probability `$P(u, v)$`

of existing. Given these probabilities, you have to find out the expected number of connected components of such a graph created according to the probabilities.

## Input

The first line contains an integer `$N$`

. After that, there are `$N$`

lines of input. The ith line has i numbers on it. jth number of ith line represents the probability `$P(i, j)$`

in **percentage**. All input numbers are integers.

`$1 \leq N \leq 17$`

`$0 \leq P(i, j) \leq 100$`

## Output

The expected number of connected components can be represented as `$P/Q$`

, where `$P$`

and `$Q$`

are natural numbers. Output `$P \times Q^{-1}$`

mod `$998244353$`

.

## Samples

Factors

| CPU | Memory | Source |
---|

Bash 5.0 | 1× | 1× | 1× |

Brainf*ck | 1× | 1× | 1× |

C# Mono 6.0 | 1× | 1× | 1× |

C++11 GCC 7.4 | 1× | 1× | 1× |

C++14 GCC 8.3 | 1× | 1× | 1× |

C++17 GCC 9.2 | 1× | 1× | 1× |

C++20 GCC 12.1 | 1× | 1× | 1× |

C11 GCC 12.1 | 1× | 1× | 1× |

C11 GCC 9.2 | 1× | 1× | 1× |

Common Lisp SBCL 2.0 | 1× | 1× | 1× |

Erlang 22.3 | 1× | 1× | 1× |

Free Pascal 3.0 | 1× | 1× | 1× |

Go 1.18 | 1× | 1× | 1× |

Haskell 8.6 | 1× | 1× | 1× |

Java 1.8 | 1× | 1× | 1× |

Kotlin 1.1 | 1× | 1× | 1× |

Lua 5.4 | 1× | 1× | 1× |

Node.js 10.16 | 1× | 1× | 1× |

Perl 5.30 | 1× | 1× | 1× |

PHP 7.2 | 1× | 1× | 1× |

PyPy 7.1 (2.7) | 1× | 1× | 1× |

PyPy 7.1 (3.6) | 1× | 1× | 1× |

Python 2.7 | 1× | 1× | 1× |

Python 3.7 | 1× | 1× | 1× |

Ruby 2.6 | 1× | 1× | 1× |

Rust 1.57 | 1× | 1× | 1× |

Swift 5.3 | 1× | 1× | 1× |

Whitespace | 1× | 1× | 1× |