A two dimensional array is called a bracket array if each grid contains one of the two possible brackets - "(" or ")". A path through the two dimensional array cells is called monotonous if any two consecutive cells in the path are side-adjacent and each cell of the path is located below or to the right from the previous one.

A two dimensional array whose size equals n \times m is called a correct bracket array, if any string formed by writing out the brackets on some monotonous way from cell (1,1) to cell (n,m) forms a correct bracket sequence.

Let's define the operation of comparing two correct bracket arrays of equal size (a and b) like that. Let's consider a given two dimensional array of priorities (c) - a two dimensional array of same size, containing different integers from 1 to nm. Let's find such position (i,j) in the two dimensional array, that ai,j \neq bi,j. If there are several such positions, let's choose the one where number ci,j is minimum. If ai,j="(", then a \lt b, otherwise a \gt b. If the position (i,j) is not found, then the arrays are considered equal.

Your task is to find a k-th two dimensional correct bracket array. It is guaranteed that for the given sizes of n and m there will be no less than k two dimensional correct bracket arrays.

The first line contains integers n, m and k - the sizes of the array and the number of the sought correct bracket array (1 \le n,m \le 100, 1 \le k \le 1018). Then an array of priorities is given, n lines each containing m numbers, number pi,j shows the priority of character j in line i (1 \le pi,j \le nm, all pi,j are different).

Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.

Print the k-th two dimensional correct bracket array.

In the first sample exists only one correct two-dimensional bracket array.

In the second and in the third samples two arrays exist.

A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters «+» and «1» into this sequence. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.