Problem:
Score : 500 points

Problem Statement

We have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.

The square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i,j} is 0, and white if S_{i,j} is 1.

We will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.

How many times do we need to cut the bar so that every block after the cuts has K or less white squares?

Constraints

1 \leq H \leq 10

1 \leq W \leq 1000

1 \leq K \leq H \times W

S_{i,j} is 0 or 1.

Input

Input is given from Standard Input in the following format:

H W K
S_{1,1}S_{1,2}...S_{1,W}
:
S_{H,1}S_{H,2}...S_{H,W}

Output

Print the number of minimum times the bar needs to be cut so that every block after the cuts has K or less white squares.

Sample Input 1

3 5 4
11100
10001
00111

Sample Output 1

2

For example, cutting between the 1-st and 2-nd rows and between the 3-rd and 4-th columns - as shown in the figure to the left - works.

Note that we cannot cut the bar in the ways shown in the two figures to the right.

Sample Input 2

3 5 8
11100
10001
00111

Sample Output 2

0

No cut is needed.

Sample Input 3

4 10 4
1110010010
1000101110
0011101001
1101000111

Sample Output 3

3

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

h,w,k= map(int, input().split())
sn = [[-1 for i in range(h)] for i in range(w)]
for y in range(0,h):
    tmp = input()
    for x in range(0,w):
        sn[x][y] = int(tmp[x:x+1])

def countWhite(lineh, linew):
    global w,h,k

    x_to=0
    y_to=0
    for areaw in range(0, len(linew) + 1):
        x_from = x_to
        if  areaw < len(linew):
            x_to = linew[areaw]-1
        else:
            x_to = w
        for areah in range(0, len(lineh) + 1):
            y_from = y_to
            if  areah < len(lineh):
                y_to = lineh[areah]-1
            else:
                y_to = h
            count = 0
            for x in range (x_from,x_to):
                for y in range (y_from,y_to):
                    count += sn[x][y]
                    if count > k:
                        return False
        y_to=0
    return True

def getLines(count,line_max,range_from=1):
    ret = []
    if count == 0:
        return [[]]
    for i in range(range_from,line_max+1):
        datas = []
        datas.append(i)
        while len(datas) != count:
            lines = getLines(count-1,line_max,i+1)
            if len(lines) > 0:
                # pr("lenelne")
                # pr(datas)
                # pr(lines)
                #
                # pr(datas)
                for line in lines:
                    tmp = datas[:]
                    tmp.extend(line)
                    if(len(tmp) == count):
                        ret.append(tmp)
                # pr(ret)
                break
            else:
                #
                break
        # pr(datas)
        if len(datas) == count:
            ret.append(datas)

    return ret

if countWhite([],[]):
    print(0)
    exit()

not_find_flg = True
line_count = lineh_count = 1
linew_count = 0
while not_find_flg:
    linehs = getLines(lineh_count,h-1)
    linews = getLines(linew_count,w-1)
    for lineh in linehs:
        break2_flg = False
        for linew in linews:
            if countWhite(lineh,linew):
                not_find_flg = False
                break2_flg = True
                break
        if break2_flg:
            break

    if not_find_flg:
        linew_count += 1
        lineh_count -= 1
        if lineh_count < 0:
            line_count += 1
            lineh_count = line_count
            linew_count = 0

print(line_count)