Angie is studying functions!

For her homework, she was asked to figure out the coefficients ~c_1, c_2, \dots, c_N, c_{N+1}~ in the following function:

~f(x)=c_1x^N+c_2x^{N-1}+\dots+c_Nx+c_{N+1}~ (All the coefficients are integers)

Angie has ~N + 1~ arbitrary integer ~(x, y)~ coordinate pairs on the polynomial, and wants you to help her find the coefficients.

Can you help her?

Input Specification

The first line of input will be ~N~ (~1 \le N \le 10^5~), the degree number of the polynomial.

The next ~N + 1~ lines will each contain a single coordinate pair ~(x, y)~ indicating that ~f(x) = y~.

The ~x~ and ~y~ values will be given modulo ~77\,309\,411\,329~, and all ~x~ values will be unique.

Output Specification

The output should contain ~N + 1~ integers, the coefficients of the polynomial in descending degree. The coefficients should be output modulo ~77\,309\,411\,329~.

Sample Input

2
0 0
1 1
2 4

Sample Output

1 0 0