Problem:
Score : 300 points

Problem Statement

We will call a string obtained by arranging the characters contained in a string a in some order, an anagram of a.

For example, greenbin is an anagram of beginner. As seen here, when the same character occurs multiple times, that character must be used that number of times.

Given are N strings s_1, s_2, \ldots, s_N. Each of these strings has a length of 10 and consists of lowercase English characters. Additionally, all of these strings are distinct. Find the number of pairs of integers i, j (1 \leq i < j \leq N) such that s_i is an anagram of s_j.

Constraints

2 \leq N \leq 10^5

s_i is a string of length 10.

Each character in s_i is a lowercase English letter.

s_1, s_2, \ldots, s_N are all distinct.

Input

Input is given from Standard Input in the following format:

N
s_1
s_2
:
s_N

Output

Print the number of pairs of integers i, j (1 \leq i < j \leq N) such that s_i is an anagram of s_j.

Sample Input 1

3
acornistnt
peanutbomb
constraint

Sample Output 1

1

s_1 = acornistnt is an anagram of s_3 = constraint. There are no other pairs i, j such that s_i is an anagram of s_j, so the answer is 1.

Sample Input 2

2
oneplustwo
ninemodsix

Sample Output 2

0

If there is no pair i, j such that s_i is an anagram of s_j, print 0.

Sample Input 3

5
abaaaaaaaa
oneplustwo
aaaaaaaaba
twoplusone
aaaabaaaaa

Sample Output 3

4

Note that the answer may not fit into a 32-bit integer type, though we cannot put such a case here.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)


#include<bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef pair<int,int> pii;
typedef vector< pii > vii;

#define ll          long long
#define ff          first
#define ss          second
#define pb          push_back
#define mkp         make_pair
#define sz          size()

#define forf(a,b,c)    for(int i=a;i<=b;i+=c)
#define forr(a,b,c)    for(int i=a;i>=b;i-=c)
#define all(a)      a.begin(),a.end()
#define mem(a,b)    memset(a,b,sizeof(a))
#define pi          2*acos(0.0)
#define End         return 0;
#define nl endl

#define scan1(a)    scanf("%d",&a)
#define scan2(a,b)  scanf("%d %d",&a,&b)
#define scan3(a,b,c)  scanf("%d %d %d",&a,&b,&c)
#define scanl(a)    scanf("%lld",&a)
#define scanll(a,b) scanf("%lld %lld",&a,&b)
#define scanlll(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)

#define print1(a)    printf("%d",a)
#define print2(a,b)  printf("%d %d",a,b)
#define print3(a,b,c)  printf("%d %d %d",a,b,c)
#define printl(a)    printf("%lld",a)
#define printll(a,b) printf("%lld %lld",a,b)
#define printlll(a,b,c) printf("%lld %lld %lld",a,b,c)

#define MAXN        100000007
#define INF 0x3f3f3f3f
bool mark[100005];vi prime;
void seive(ll N){for(int i=2;i<=N;i++){if(mark[i]==false){prime.pb(i);for(int j=i+i;j<N;j+=i)mark[j]=true;}}}
//freopen("input.txt", "r", stdin);

int main()
{
   ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int n;
    cin>>n;
    ll sum=0;
    vector<string> v;
    for(int i=0;i<n;i++){
        string s; cin>>s;
        v.pb(s);
    }
    for(int i=0;i<n;i++) sort(all(v[i]));

    sort(all(v));

    int cnt=1,pos=1;
    for(int i=1;i<n;i++){
        if(v[i]==v[i-1]) cnt++;
        else {
            if(cnt!=1){
                    cnt--;
                sum+=((cnt*cnt+cnt)/2);
            }
            cnt=1;
        }
    }
    if(cnt!=1){
                cnt--;
                sum+=((cnt*cnt+cnt)/2);
            }
            cout<<sum<<endl;
}