Problem: Making Lunch Boxes

Taro has been hooked on making lunch boxes recently. Taro has obtained a new lunch box recipe book today, and wants to try as many of the recipes listed in the book as possible.

Enough of the ingredients for all the recipes are at hand, but they all are in vacuum packs of two. If only one of them is used leaving the other, the leftover will be rotten easily, but making two of the same recipe is not interesting. Thus he decided to make a set of lunch boxes, each with different recipe, that wouldn't leave any unused ingredients.

Note that the book may include recipes for different lunch boxes made of the same set of ingredients.

How many lunch box recipes can Taro try today at most following his dogma?

Input

The input consists of at most 50 datasets, each in the following format.


n m
b1,1...b1,m
...
bn,1...bn,m


The first line contains n, which is the number of recipes listed in the book, and m, which is the number of ingredients. Both n and m are positive integers and satisfy 1 ≤ n ≤ 500, 1 ≤ m ≤ 500 and 1 ≤ n × m ≤ 500. The following n lines contain the information for each recipe with the string of length m consisting of 0 or 1. bi,j implies whether the i-th recipe needs the j-th ingredient. 1 means the ingredient is needed for the recipe and 0 means not. Each line contains at least one 1.

The end of the input is indicated by a line containing two zeros.

Output

For each dataset, output the maximum number of recipes Taro can try.

Sample Input


4 3
110
101
011
110
7 1
1
1
1
1
1
1
1
4 5
10000
01000
00100
00010
6 6
111111
011000
100000
000010
100001
100100
0 0


Output for the Sample Input


3
6
0
6






Example

Input

4 3
110
101
011
110
7 1
1
1
1
1
1
1
1
4 5
10000
01000
00100
00010
6 6
111111
011000
100000
000010
100001
100100
0 0


Output

3
6
0
6

Solution (in PYTHON3):

Solution:
#2006_D
"""
import sys
from collections import defaultdict
def dfs(d,y,x,f):
    global ans
    if d >= 10:
        return
    f_ = defaultdict(int)
    for i in f.keys():
        f_[i] = f[i]
    for t,s in vr[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if s == x+1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t,s-1,f_)
            f_[(t,s)] = 1
            break

    for t,s in vl[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if s == x-1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t,s+1,f_)
            f_[(t,s)] = 1
            break

    for t,s in vd[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if t == y+1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t-1,s,f_)
            f_[(t,s)] = 1
            break

    for t,s in vu[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if t == y-1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t+1,s,f_)
            f_[(t,s)] = 1
            break
    return
while 1:
    w,h = map(int, sys.stdin.readline()[:-1].split())
    if w == h == 0:
        break
    a = [list(map(int, sys.stdin.readline()[:-1].split())) for i in range(h)]
    vr = defaultdict(list)
    vl = defaultdict(list)
    vd = defaultdict(list)
    vu = defaultdict(list)
    f = defaultdict(int)
    for y in range(h):
        for x in range(w):
            if a[y][x] == 1:
                f[(y,x)] = 1
            if a[y][x] in [1,3]:
                for x_ in range(x):
                    vr[(y,x_)].append((y,x))
            elif a[y][x] == 2:
                sy,sx = y,x
    for y in range(h):
        for x in range(w)[::-1]:
            if a[y][x] in (1,3):
                for x_ in range(x+1,w):
                    vl[(y,x_)].append((y,x))
    for x in range(w):
        for y in range(h):
            if a[y][x] in (1,3):
                for y_ in range(y):
                    vd[(y_,x)].append((y,x))
    for x in range(w):
        for y in range(h)[::-1]:
            if a[y][x] in (1,3):
                for y_ in range(y+1,h):
                    vu[(y_,x)].append((y,x))
    ind = [[[0]*4 for i in range(w)] for j in range(h)]
    ans = 11
    dfs(0,sy,sx,f)
    ans = ans if ans < 11 else -1
    print(ans)
"""

#2018_D
"""
import sys
from collections import defaultdict
sys.setrecursionlimit(1000000)

def dfs(d,s,l,v,dic):
    s_ = tuple(s)
    if dic[(d,s_)] != None:
        return dic[(d,s_)]
    if d == l:
        dic[(d,s_)] = 1
        for x in s:
            if x > (n>>1):
                dic[(d,s_)] = 0
                return 0
        return 1
    else:
        res = 0
        i,j = v[d]
        if s[i] < (n>>1):
            s[i] += 1
            res += dfs(d+1,s,l,v,dic)
            s[i] -= 1
        if s[j] < (n>>1):
            s[j] += 1
            res += dfs(d+1,s,l,v,dic)
            s[j] -= 1
        dic[(d,s_)] = res
        return res

def solve(n):
    dic = defaultdict(lambda : None)
    m = int(sys.stdin.readline())
    s = [0]*n
    f = [[1]*n for i in range(n)]
    for i in range(n):
        f[i][i] = 0
    for i in range(m):
        x,y = [int(x) for x in sys.stdin.readline().split()]
        x -= 1
        y -= 1
        s[x] += 1
        f[x][y] = 0
        f[y][x] = 0
    v = []
    for i in range(n):
        for j in range(i+1,n):
            if f[i][j]:
                v.append((i,j))
    l = len(v)
    print(dfs(0,s,l,v,dic))

while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""
#2011_D
"""
import sys
def dfs(s,d,f,v):
    global ans
    if ans == n-n%2:
        return
    if d > ans:
        ans = d
    for i in range(n):
        if s[i] == 0:
            for j in range(i+1,n):
                if s[j] == 0:
                    if f[i] == f[j]:
                        s[i] = -1
                        s[j] = -1
                        for k in v[i]:
                            s[k] -= 1
                        for k in v[j]:
                            s[k] -= 1
                        dfs(s,d+2,f,v)
                        s[i] = 0
                        s[j] = 0
                        for k in v[i]:
                            s[k] += 1
                        for k in v[j]:
                            s[k] += 1

def solve(n):
    p = [[int(x) for x in sys.stdin.readline().split()] for i in range(n)]
    v = [[] for i in range(n)]
    f = [0]*n
    s = [0]*n
    for i in range(n):
        x,y,r,f[i] = p[i]
        for j in range(i+1,n):
            xj,yj,rj,c = p[j]
            if (x-xj)**2+(y-yj)**2 < (r+rj)**2:
                v[i].append(j)
                s[j] += 1
    dfs(s,0,f,v)
    print(ans)
while 1:
    n = int(sys.stdin.readline())
    ans = 0
    if n == 0:
        break
    solve(n)
"""

#2003_D
"""
import sys
def root(x,par):
    if par[x] == x:
        return x
    par[x] = root(par[x],par)
    return par[x]

def unite(x,y,par,rank):
    x = root(x,par)
    y = root(y,par)
    if rank[x] < rank[y]:
        par[x] = y
    else:
        par[y] = x
        if rank[x] == rank[y]:
            rank[x] += 1

def solve(n):
    p = [[float(x) for x in sys.stdin.readline().split()] for i in range(n)]
    v = []
    for i in range(n):
        for j in range(i):
            xi,yi,zi,ri = p[i]
            xj,yj,zj,rj = p[j]
            d = max(0,((xi-xj)**2+(yi-yj)**2+(zi-zj)**2)**0.5-(ri+rj))
            v.append((i,j,d))
    par = [i for i in range(n)]
    rank = [0]*n
    v.sort(key = lambda x:x[2])
    ans = 0
    for x,y,d in v:
        if root(x,par) != root(y,par):
            unite(x,y,par,rank)
            ans += d
    print("{:.3f}".format(round(ans,3)))

while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""

#2009_D
"""
import sys
from heapq import heappop,heappush
from collections import defaultdict
def solve(n,m):
    s,g = [int(x) for x in sys.stdin.readline().split()]
    s -= 1
    g -= 1
    e = [[] for i in range(n)]
    for i in range(m):
        a,b,d,c = [int(x) for x in sys.stdin.readline().split()]
        a -= 1
        b -= 1
        e[a].append((b,d,c))
        e[b].append((a,d,c))
    dist = defaultdict(lambda : float("inf"))
    dist[(s,0,-1)] = 0
    q = [(0,s,0,-1)]
    while q:
        dx,x,v,p = heappop(q)
        if x == g and v == 1:
            print(dx)
            return
        for i in range(-1,2):
            v_ = v+i
            if v_ < 1 :continue
            for y,d,c in e[x]:
                if p == y:
                    continue
                if v_ > c:
                    continue
                z = d/v_
                if dx+z < dist[(y,v_,x)]:
                    dist[(y,v_,x)] = dx+z
                    heappush(q,(dist[(y,v_,x)],y,v_,x))
    print("unreachable")
    return

while 1:
    n,m = [int(x) for x in sys.stdin.readline().split()]
    if n == 0:
        break
    solve(n,m)
"""

#2016_D
"""
import sys
def solve(n):
    w = [int(x) for x in sys.stdin.readline().split()]
    dp = [[0]*(n+1) for i in range(n+1)]
    for le in range(n+1):
        for l in range(n):
            r = l+le
            if r > n:break
            if not (r-l)%2 and abs(w[l]-w[r-1]) < 2:
                if dp[l+1][r-1] == r-l-2:
                    dp[l][r] = r-l
                    continue
            for k in range(l+1,r):
                if dp[l][k] + dp[k][r] > dp[l][r]:
                    dp[l][r] = dp[l][k] + dp[k][r]
    print(dp[0][n])
while 1:
    n = int(sys.stdin.readline())
    if not n:
        break
    solve(n)
"""
#2009_D
"""
alp = list("abcdefghijklmnopqrstuvwxyz")
c = {}
key = {}
for i in range(25):
    c[alp[i]] = alp[i+1]
    key[alp[i]] = i
key["z"] = 25

def dfs(i,k,f,n):
    global ans
    if i == n:
        for j in k:
            if f[key[j]]:
                break
        else:
            ans.append(k)
    else:
        dfs(i+1,k+s[i],f,n)
        if s[i] != "z" and f[key[s[i]]+1]:
            f[key[s[i]]+1] = 0
            dfs(i+1,k+c[s[i]],f,n)
            f[key[s[i]]+1] = 1

def solve(s):
    global ans
    n = len(s)
    d = {}
    for i in s:
        d[i] = 1
    f = [1]*26
    f[0] = 0
    dfs(0,"",f,n)
    ans.sort()
    print(len(ans))
    if len(ans) < 10:
        for i in ans:
            print(i)
    else:
        for i in ans[:5]:
            print(i)
        for i in ans[-5:]:
            print(i)
while 1:
    s = input()
    ans = []
    if s == "#":
        break
    solve(s)
"""

#2004_D
"""
import sys
from collections import defaultdict
while 1:
    d = defaultdict(list)
    d_ = defaultdict(list)
    n = int(sys.stdin.readline())
    if n == 0:break
    point = [[float(x) for x in sys.stdin.readline().split()] for i in range(n)]
    ans = 1
    for i in range(n):
        p,q = point[i]
        for j in range(n):
            if i == j:continue
            s,t = point[j]
            if (p-s)**2+(q-t)**2 > 4:
                continue
            d[i].append(j)
            if j > i:
                d_[i].append(j)

    for i in range(n):
        p,q = point[i]
        for j in d_[i]:
            s,t = point[j]
            v = (t-q,p-s)
            m = ((p+s)/2,(q+t)/2)
            l = 0
            r = 10000
            while r-l > 0.0001:
                k = (l+r)/2
                a,b = m[0]+k*v[0],m[1]+k*v[1]
                if (p-a)**2+(q-b)**2 < 1:
                    l = k
                else:
                    r = k
            ans_ = 2
            for l in d[i]:
                if l == j:
                    continue
                x,y = point[l]
                if (x-a)**2+(y-b)**2 < 1:
                    ans_ += 1

            if ans_ > ans:
                ans = ans_
                if ans == n:break

            k = -k
            a,b = m[0]+k*v[0],m[1]+k*v[1]
            ans_ = 2
            for l in d[i]:
                if l == j:
                    continue
                x,y = point[l]
                if (x-a)**2+(y-b)**2 < 1:
                    ans_ += 1

            if ans_ > ans:
                ans = ans_
                if ans == n:break
        if ans == n:break
    print(ans)
"""
#2010_D
"""
import sys
from collections import defaultdict,deque
d = [(1,0),(-1,0),(0,1),(0,-1)]
def bfs(b,a,k):
    q = deque([(b,a)])
    bfs_map[b][a] = k
    g = a+0.5
    p = s[b][a]
    su = 1
    while q:
        y,x = q.popleft()
        for dy,dx in d:
            y_ = y+dy
            x_ = x+dx
            if 0 <= y_ < h and 0 <= x_ < w:
                if bfs_map[y_][x_] < 0 and s[y_][x_] == p:
                    bfs_map[y_][x_] = k
                    q.append((y_,x_))
                    g += x_+0.5
                    su += 1
    f[k] = (g,su)

def dfs(x):
    if g[x] != None:
        return g[x]
    g[x] = [f[x][0],f[x][1]]
    for y in v[x]:
        g_ = dfs(y)
        g[x][0] += g_[0]
        g[x][1] += g_[1]
    return g[x]

while 1:
    w,h = [int(x) for x in sys.stdin.readline().split()]
    if w == 0:
        break
    s = [sys.stdin.readline()[:-1] for i in range(h)]
    f = defaultdict(lambda : 0)
    bfs_map = [[-1]*w for i in range(h)]
    k = 0
    for y in range(h)[::-1]:
        for x in range(w):
            if s[y][x] != "." and bfs_map[y][x] < 0:
                bfs(y,x,k)
                k += 1

    v = [[] for i in range(k)]
    l = [float("inf")]*k
    r = [0]*k
    fl = [1]*k

    for y in range(h):
        for x in range(w):
            if bfs_map[y][x] > -1:
                b = bfs_map[y][x]
                if y == h-1 or (bfs_map[y+1][x] != b and bfs_map[y+1][x] > -1):
                    l[b] = min(l[b],x)
                    r[b] = max(r[b],x+1)
                    if y < h-1 and fl[b]:
                        v[bfs_map[y+1][x]].append(b)
                        fl[b] = 0
    g = [None]*k
    for i in range(k):
        dfs(i)
        gx = g[i][0]/g[i][1]
        if gx <= l[i] or r[i] <= gx:
            print("UNSTABLE")
            break
    else:
        print("STABLE")
"""

#2015_D
"""
import sys
def solve(n):
    p = [int(sys.stdin.readline()) for i in range(n)]
    dp = [[[-1,-1] for c in range(1000)] for i in range(n)]
    dp[-1][0] = [0,0]
    for i in range(n):
        e = -p[i]%1000
        for c in range(1000):
            if dp[i-1][c][0] != -1:
                cost = 1 if c+e > 499 else 0
                k = (c+e-500)%1000 if cost else (c+e)%1000
                if dp[i][k] < [dp[i-1][c][0]+cost,dp[i-1][c][1]-p[i]]:
                    dp[i][k] = [dp[i-1][c][0]+cost,dp[i-1][c][1]-p[i]]

                if dp[i][c] < [dp[i-1][c][0],dp[i-1][c][1]]:
                    dp[i][c] = [dp[i-1][c][0],dp[i-1][c][1]]
    ans = [0,-1]
    for i in range(1000):
        if dp[-1][i] > ans:
            ans[0] = dp[-1][i][0]
            ans[1] = dp[-1][i][1]
    print(ans[0],-ans[1])
while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""
#2017_D
import sys
from collections import defaultdict

def solve(n,m):
    b = [int(sys.stdin.readline(),2) for i in range(n)]
    if n < m:
        M = 1<<n
        ans = 0
        for i in range(M):
            k = 0
            s = 0
            for j in range(n):
                if i&(1<<j):
                    k ^= b[j]
                    s += 1
            if not k:
                if s > ans:
                    ans = s
        print(ans)
    else:
        dp = defaultdict(lambda : 0)
        dp[0] = 0
        for i in b:
            d = dp.copy()
            for j in d.keys():
                j_ = i^j
                if d[j]+1 > dp[j_]:
                    dp[j_] = d[j]+1
        print(dp[0])
while 1:
    n,m = [int(x) for x in sys.stdin.readline().split()]
    if n == 0:
        break
    solve(n,m)