### BUGGY CODE ###

#import numpy as np
from copy import deepcopy
import sys, math
from itertools import permutations, combinations
from collections import defaultdict, Counter, deque
from math import factorial#, gcd
from bisect import bisect_left #bisect_left(list, value)
sys.setrecursionlimit(10**7)
enu = enumerate
MOD = 10**9+7
def input(): return sys.stdin.readline()[:-1]
def pri(x): print('\n'.join(map(str, x)))

H, W, K = map(int, input().split())
SHW = [list(map(int, list(input()))) for _ in range(H)]
tSHW = list(zip(*SHW))

def vcut(cuts: list):
    num = 0
    cuts = [0] + cuts + [H]

    iparts = [0]*(len(cuts)-1)
    parts = deepcopy(iparts)
    w = 0
    while w < W:
        for i, (sc, ec) in enu(zip(cuts, cuts[1:])):
            if K < parts[i]+sum(tSHW[w][sc:ec]):
                num += 1
                parts = deepcopy(iparts)
                break
            else:
                parts[i] += sum(tSHW[w][sc:ec])
        else:
            w += 1
    return num

res = (H-1)*(W-1)
for i in range(2**(H-1)):
    cnt = 0
    cuts = [] # cut index
    for j in range((H-1)):
        if ((i >> j) & 1):
            cnt += 1
            cuts.append(j+1)
    if res > cnt:
        cnt += vcut(cuts)
        if res > cnt:
            res = cnt

print(res)



### FIXED CODE ###

def main():
    #import numpy as np
    import sys, math
    from itertools import permutations, combinations
    from collections import defaultdict, Counter, deque
    from math import factorial#, gcd
    from bisect import bisect_left #bisect_left(list, value)
    sys.setrecursionlimit(10**7)
    enu = enumerate
    MOD = 10**9+7
    def input(): return sys.stdin.readline()[:-1]
    pl = lambda x: print(*x, sep='\n')

    H, W, K = map(int, input().split())
    S = [list(map(int, list(input()))) for _ in range(H)]

    from copy import deepcopy
    cS = [[0]*(W+1) for _ in range(H+1)]
    # cS = deepcopy(S)

    for h in range(1, H+1):
        for w in range(W):
            cS[h][w+1] = cS[h][w] + S[h-1][w]
    for w in range(1, W+1):
        for h in range(H):
            cS[h+1][w] = cS[h][w] + cS[h+1][w]
    # pl(cS)

    mcut = 10**9
    for i in range(2**(H-1)):
        yoko = []
        for j in range(H):
            if ((i >> j) & 1):
                yoko.append(j+1)
        yoko = [0] + yoko + [H]
        # yoko.append(H)
        # print(yoko)
        
        cut = len(yoko)-2
        lastcut = 0 # index-w
        w = 1
        cannot = False
        while w < W+1:
            if cannot:
                w = W + 100
                break
            for ind, y in enu(yoko):
                if ind == 0:
                    continue
                v1 = cS[y][w]
                v2 = cS[yoko[ind-1]][w]
                v3 = cS[yoko[ind-1]][lastcut]
                v4 = cS[y][lastcut]
                val = v1 - v2 + v3 - v4
                # print('  v1, v2', v1, v2)
                if K < val:
                    cut += 1
                    if lastcut == w-1:
                        cannot = True
                    lastcut = w-1
                    break
            else:
                w += 1
            # print(' val', val)
        if not(cannot) and cut < mcut:
            # print('yoko', yoko)
            mcut = cut

    print(mcut)
if __name__ == '__main__':
    main()