Problem Statement

16 fighters compete in a one-on-one tournament.

The fighters are assigned numbers from 1 to 16.

Fighters have matchups, and a table gives which fighter wins when any two fighters face each other.

The tournament is a complete binary tree.

A simulation is to be run in order to measure each fighter's win rate.
When every possible first-round arrangement is tried, running each one through to the end of the final, output the number of times each fighter wins the tournament, one per line, for fighters 1 to 16.

Arrangements are considered different if their order in the first round differs, even if the matchups are the same.
That is, a total of 16! first-round arrangements are considered.

Input

$a_{(1,1)}$ $\dots$ $a_{(1,16)}$
$\dots$
$a_{(j,1)}$ $\dots$ $a_{(j,16)}$
$\dots$
$a_{(16,1)}$ $\dots$ $a_{(16,16)}$

To see which fighter wins when fighter number i and fighter number j fight, look at row j, column i of the table: if it is 1, j wins, and if it is -1, i wins. The lower-left half of the table is filled with 0 as dummy data to make the input easier to read. That is, only the part of the table with j < i is meaningful. Find ansi, the number of times fighter number i wins the tournament when all first-round arrangements are tried.

Output

$ans_1$
$\dots$
$ans_i$
$\dots$
$ans_{16}$
Print a newline at the end.

Sample

0 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 1
0 0 1 1 -1 1 1 -1 1 1 -1 -1 -1 1 1 1
0 0 0 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1
0 0 0 0 -1 1 -1 1 -1 1 1 1 -1 1 -1 -1
0 0 0 0 0 1 -1 1 -1 -1 1 -1 -1 1 -1 -1
0 0 0 0 0 0 1 -1 1 -1 1 1 1 1 -1 1
0 0 0 0 0 0 0 1 1 1 1 1 1 1 -1 1
0 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 1 -1
0 0 0 0 0 0 0 0 0 1 1 -1 -1 1 1 -1
0 0 0 0 0 0 0 0 0 0 1 -1 1 1 -1 1
0 0 0 0 0 0 0 0 0 0 0 1 1 -1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1613069320192
2902313238528
119390961664
507047542784
1339820638208
1069828669440
7688706785280
1315405791232
367798026240
590398128128
1159765950464
311637147648
146366988288
7884701696
1659518025728
123837972480