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. 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. 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 brack