CF32D.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.

伯兰德的星图是一张 $n \times m$ 的方格图。每个方格中要么有一颗星，要么没有星。所有伯兰德天文学家最喜爱的星座是“十字星座”。该星座可由任意 5 颗星构成，使得对某个整数 $x$（该星座的半径），满足以下条件：

• 第 2 颗星与第 1 颗星位于同一竖直线上，但在第 1 颗星正上方 $x$ 格；
• 第 3 颗星与第 1 颗星位于同一竖直线上，但在第 1 颗星正下方 $x$ 格；
• 第 4 颗星与第 1 颗星位于同一水平线上，但在第 1 颗星正左方 $x$ 格；
• 第 5 颗星与第 1 颗星位于同一水平线上，但在第 1 颗星正右方 $x$ 格。

这类星座可能数量极多，因此按如下规则用从 1 开始的整数为其编号：比较两个星座时，半径较小者编号更小；若半径相等，则中心星（即第 1 颗星）行号更小（即位置更高）者编号更小；若中心星行号也相同，则中心星列号更小（即位置更靠左）者编号更小。

你的任务是：给定一张伯兰德星图，找出编号为 $k$ 的星座。

The first line contains three integers n, m and k (1 ≤ n, m ≤ 300, 1 ≤ k ≤ 3·107) — 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.

第一行包含三个整数 $n$、$m$ 和 $k$（$1 \leq n, m \leq 300$，$1 \leq k \leq 3 \cdot 10^7$），分别表示地图的高度、宽度以及所要求的星座的编号。左上角坐标为 $(1, 1)$，右下角坐标为 $(n, m)$。接下来是 $n$ 行，每行 $m$ 个字符，描述该地图。第 $i$ 行的第 $j$ 个字符为 *，表示对应位置有一颗星；为 .，表示该位置为空。

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.

如果星座的数量少于 $k$，则输出 $-1$。否则输出 $5$ 行，每行两个整数——所求星座的各星坐标。按以下顺序输出各星：中心星、上方星、下方星、左方星、右方星。