# World Championship

Woods in the spring. 1884. Landscape differs fine gradation of color, freedom and diversity of artistic methods, while maintaining a rigorous, realistic exact figure.

In the finals of the World Cup in France involved 16 teams. The winner is determined on the Olympic system:

Known probability of winning (percentage) of each team in each group. Necessary for each team to calculate the probability that she wins the tournament (will become the champion of the world).

## Input

Consists of several tests. The first line of each test contains a number of teams in the league n (4 ≤ n ≤ 64, n is a power of two). The following n lines describe the names of teams, each of which contains no more than 10 characters. The following is a matrix of probabilities p size n × n. Cell p[i][j] contains a non-negative integer value is the probability of a percentage, to which i-th team will win in the j-th. It is obvious that p[i][j] + p[j][i] = 100%.

## Output

For each test case print its number. For each team find the probability (in percents) to become a World Champion. Print the countries in the same order as they given in the input. Print the team names left-justified in a field of 10 characters. After each country name print one space and the percent probability to win the cup as shown below.