F1. Marek and Matching (easy version)time limit per test7 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is an easier version of the problem. In this version, n \le 6.Marek is working hard on creating strong testcases to his new algorithmic problem. You want to know what it is? Nah, we're not telling you. However, we can tell you how he generates the testcases.Marek chooses an integer n and n^2 integers p_{ij} (1 \le i \le n, 1 \le j \le n). He then generates a random bipartite graph with 2n vertices. There are n vertices on the left side: \ell_1, \ell_2, \dots, \ell_n, and n vertices on the right side: r_1, r_2, \dots, r_n. For each i and j, he puts an edge between vertices \ell_i and r_j with probability p_{ij} percent.It turns out that the tests will be strong only if a perfect matching exists in the generated graph. What is the probability that this will occur?It can be shown that this value can be represented as \frac{P}{Q} where P and Q are coprime integers and Q \not\equiv 0 \pmod{10^9+7}. Let Q^{-1} be an integer for which Q \cdot Q^{-1} \equiv 1 \pmod{10^9+7}. Print the value of P \cdot Q^{-1} modulo 10^9+7.InputThe first line of the input contains a single integer n (\mathbf{1 \le n \le 6}). The following n lines describe the probabilities of each edge appearing in the graph. The i-th of the lines contains n integers p_{i1}, p_{i2}, \dots, p_{in} (0 \le p_{ij} \le 100); p_{ij} denotes the probability, in percent, of an edge appearing between \ell_i and r_j.OutputPrint a single integer — the probability that the perfect matching exists in the bipartite graph, written as P \cdot Q^{-1} \pmod{10^9+7} for P, Q defined above.ExamplesInput
2
50 50
50 50
Output
937500007
Input
3
3 1 4
1 5 9
2 6 5
Output
351284554
NoteIn the first sample test, each of the 16 graphs below is equally probable. Out of these, 7 have a perfect matching:  Therefore, the probability is equal to \frac{7}{16}. As 16 \cdot 562\,500\,004 = 1 \pmod{10^9+7}, the answer to the testcase is 7 \cdot 562\,500\,004 \mod{(10^9+7)} = 937\,500\,007.
2
50 50
50 50

937500007 
['brute force', 'probabilities', '*3100']