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C. Brackets

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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.

Examples

Input

1 2 1

1 2

Output

()

Input

2 3 1

1 2 3

4 5 6

Output

(()

())

Input

3 2 2

3 6

1 4

2 5

Output

()

)(

()

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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