Panda is preparing for the mid-term examination by reading his notebook. However, some parts of his notebook have been ruined and some data are lost. For example, when he encounter a list of functions, he find out that all parameters are lost. The functions are similiar and can be written as

y = exp(a₀x) + exp(a₁x) + ... + exp(a₉x).

Although all the a_i are lost, the coordinates of some points on the curve of the function are known. Can you find back all the a_i with these coordinates? Notice that all the a_i are positive integers no more than 10 and a_i ≤ a_i+1 (i=0,1,...,8). It is guaranteed to been only one correct answer.

The first line of input is N, the number of the coordinates.
Each of the next N lines contains a pair of coordinates x_i, y_i separated by one space.

1 ≤ N ≤ 20
0 ≤ x_i ≤ 5

The output contains 10 lines, each contains one a_i in ascending order.