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*<sub class="lower-index">*i*, *j*</sub> ≠ *b*<sub class="lower-index">*i*, *j*</sub>. If there are several such positions, let's choose the one where number *c*<sub class="lower-index">*i*, *j*</sub> is minimum. If *a*<sub class="lower-index">*i*, *j*</sub> = "(", 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 ≤ *n*, *m* ≤ 100, 1 ≤ *k* ≤ 10<sup class="upper-index">18</sup>). Then an array of priorities is given, *n* lines each containing *m* numbers, number *p*<sub class="lower-index">*i*, *j*</sub> shows the priority of character *j* in line *i* (1 ≤ *p*<sub class="lower-index">*i*, *j*</sub> ≤ *nm*, all *p*<sub class="lower-index">*i*, *j*</sub> 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.
print("_RANDOM_GUESS_1690486262.3801467")# 1690486262.3801653