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 $*n* × *m*$ 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 $*a*_{*i*, *j*} ≠ *b*_{*i*, *j*}$. If there are several such positions, let's choose the one where number $*c*_{*i*, *j*}$ is minimum. If $*a*_{*i*, *j*} =$"(", then $*a* < *b*$, otherwise $*a* > *b*$. 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.

Input

The first line contains integers $*n*$, $*m*$ and $*k*$ — the sizes of the array and the number of the sought correct bracket array ($1 ≤ *n*, *m* ≤ 100$, $1 ≤ *k* ≤ 10^{18}$). Then an array of priorities is given, $*n*$ lines each containing $*m*$ numbers, number $*p*_{*i*, *j*}$ shows the priority of character $*j*$ in line $*i*$ ($1 ≤ *p*_{*i*, *j*} ≤ *nm*$, all $*p*_{*i*, *j*}$ are different).

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

Output

Print the $*k*$-th two dimensional correct bracket array.

Note

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.