A7956 | Constellation

A star map in Berland is a checked field $n×m$ squares. In each square there is or there is not a star. The favourite constellation of all Berland's astronomers is the constellation of the Cross. This constellation can be formed by any 5 stars so, that for some integer $x$ (radius of the constellation) the following is true:

- the 2nd is on the same vertical line as the 1st, but $x$ squares up
- the 3rd is on the same vertical line as the 1st, but $x$ squares down
- the 4th is on the same horizontal line as the 1st, but $x$ squares left
- the 5th is on the same horizontal line as the 1st, but $x$ squares right

Such constellations can be very numerous, that's why they are numbered with integers from 1 on the following principle: when two constellations are compared, the one with a smaller radius gets a smaller index; if their radii are equal — the one, whose central star if higher than the central star of the other one; if their central stars are at the same level — the one, whose central star is to the left of the central star of the other one.

Your task is to find the constellation with index $k$ by the given Berland's star map.

The first line contains three integers $n$ , $m$ and $k$ ( $1<=n,m<=300,1<=k<=3·10^{7}$ ) — height and width of the map and index of the required constellation respectively. The upper-left corner has coordinates $(1,1)$ , and the lower-right — $(n,m)$ . Then there follow $n$ lines, $m$ characters each — description of the map. $j$ -th character in $i$ -th line is «\*», if there is a star in the corresponding square, and «.» if this square is empty.

If the number of the constellations is less than $k$ , output -1. Otherwise output 5 lines, two integers each — coordinates of the required constellation. Output the stars in the following order: central, upper, lower, left, right.