CF152C： Pocket Book（思维）

C. Pocket Book

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

One day little Vasya found mom's pocket book. The book had n names of her friends and unusually enough, each name was exactly mletters
long. Let's number the names from 1 to n in
the order in which they are written.

As mom wasn't home, Vasya decided to play with names: he chose three integers i, j, k (1 ≤ i < j ≤ n, 1 ≤ k ≤ m),
then he took names number i and j and
swapped their prefixes of length k. For example, if we take names "CBDAD"
and "AABRD" and swap their prefixes with the length of 3,
the result will be names "AABAD" and "CBDRD".

You wonder how many different names Vasya can write instead of name number 1, if Vasya is allowed to perform any number of the described actions.
As Vasya performs each action, he chooses numbers i, j, k independently
from the previous moves and his choice is based entirely on his will. The sought number can be very large, so you should only find it modulo 1000000007 (109 + 7).

Input

The first input line contains two integers n and m (1 ≤ n, m ≤ 100)
— the number of names and the length of each name, correspondingly. Then n lines contain names, each name consists of exactly m uppercase
Latin letters.

Output

Print the single number — the number of different names that could end up in position number 1 in the pocket book after the applying the procedures
described above. Print the number modulo 1000000007 (109 + 7).

Examples

input

2 3
AAB
BAA

output

4

input

4 5
ABABA
BCGDG
AAAAA
YABSA

output

216

Note

In the first sample Vasya can get the following names in the position number 1: "AAB", "AAA", "BAA" and "BAB".

题意：給N个字符串，每个长度为M，每次可以交换任意两个串的任意长度前缀，问位置1可以出现几个不同的字符串。

思路：可以证明N个串的第i个字符都可以出现在这N个串的第i位，那么统计下每个位有几个不同字符，乘起来即可。

# include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL mod = 1e9+7;
unordered_set<char>s[103];
int main()
{
int n, m;
char ss[103];
scanf("%d%d",&n,&m);
for(int i=1; i<=n; ++i)
{
scanf("%s",ss+1);
for(int i=1; i<=m; ++i)
s[i].insert(ss[i]);
}
LL ans = 1;
for(int i=1; i<=m; ++i)
ans = ans*(s[i].size())%mod;
printf("%lld\n",ans);
return 0;
}