We want to encode a given string $S$ to a binary string. Each alphabet character in $S$ should be mapped to a different variable-length code and the code must not be a prefix of others.

Huffman coding is known as one of ways to obtain a code table for such encoding.

For example, we consider that appearance frequencycies of each alphabet character in $S$ are as follows:

| a| b| c| d| e| f
---|---|---|---|---|---|---
freq.| 45| 13| 12| 16| 9| 5
code| 0| 101| 100| 111| 1101| 1100

We can obtain "Huffman codes" (the third row of the table) using Huffman's algorithm.

The algorithm finds a full binary tree called "Huffman tree" as shown in the following figure.

<image>

To obtain a Huffman tree, for each alphabet character, we first prepare a node which has no parents and a frequency (weight) of the alphabet character. Then, we repeat the following steps:

1. Choose two nodes, $x$ and $y$, which has no parents and the smallest weights.
2. Create a new node $z$ whose weight is the sum of $x$'s and $y$'s.
3. Add edge linking $z$ to $x$ with label $0$ and to $y$ with label $1$. Then $z$ become their parent.
4. If there is only one node without a parent, which is the root, finish the algorithm. Otherwise, go to step 1.



Finally, we can find a "Huffman code" in a path from the root to leaves.

Task

Given a string $S$, output the length of a binary string obtained by using Huffman coding for $S$.

Constraints

* $1 \le |S| \le 10^5$
* $S$ consists of lowercase English letters.

Input


$S$


A string $S$ is given in a line.

Output

Print the length of a binary string in a line.

Examples

Input

abca


Output

6


Input

aaabbcccdeeeffg


Output

41


Input

z


Output

1
#include "bits/stdc++.h"
 
using namespace std;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef vector<PII> VPII;
typedef long long LL;
typedef priority_queue<int> PQ_DESC;
typedef priority_queue<int, vector<int>, greater<int>> PQ_ASC;
typedef priority_queue<PII> PQ_DESC_PII;
typedef priority_queue<PII, vector<PII>, greater<PII>> PQ_ASC_PII;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<VVLL> VVVLL;

#define SORT_ASC(c) sort((c).begin(), (c).end())
#define SORT_DESC(c) sort((c).begin(), (c).end(), greater<typeof((c).begin())>())
 
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)
#define FORL(i,a,b) for(LL i=(a);i<(b);++i)
#define REPL(i,n)  FORL(i,0,n)
#define ALL(a) (a).begin(),(a).end()
 
const double EPS = 1e-10;
const double PI  = acos(-1.0);

 //debug func
template<typename T>
void vprint(vector<T> v) {
    for(auto x : v) {
        cerr << x << " ";
    }
    cerr << endl;
}
 
template<typename T>
void vvprint(vector<vector<T>> vv) {
    REP(i, vv.size()) {
        REP(j, vv[i].size()) {
            cerr << vv[i][j] << " ";
        }
        cerr << endl;
    }
}

template <typename Iterator>
inline bool next_combination(const Iterator first, Iterator k, const Iterator last)
{
   /* Credits: Thomas Draper */
   if ((first == last) || (first == k) || (last == k))
      return false;
   Iterator itr1 = first;
   Iterator itr2 = last;
   ++itr1;
   if (last == itr1)
      return false;
   itr1 = last;
   --itr1;
   itr1 = k;
   --itr2;
   while (first != itr1)
   {
      if (*--itr1 < *itr2)
      {
         Iterator j = k;
         while (!(*itr1 < *j)) ++j;
         iter_swap(itr1,j);
         ++itr1;
         ++j;
         itr2 = k;
         rotate(itr1,j,last);
         while (last != j)
         {
            ++j;
            ++itr2;
         }
         rotate(k,itr2,last);
         return true;
      }
   }
   rotate(first,k,last);
   return false;
}

inline double get_time_sec(void){
    return static_cast<double>(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count())/1000000000;
}

template<typename T>
T lcm(T a, T b) {
    return (a / __gcd(a, b)) * b;
}

template<typename T>
map<T, T> prime_list(T n) {
    map<T, T> ret;
    for(T i = 2; i*i <= n; i++) {
        if(n % i == 0) {
            ret[i] = 0;
            while(n % i == 0) {
                n /= i;
                ret[i]++;
            }
        }
    }
    if(n != 1) ret[n]++;
    return ret;
}

#define MOD 1000000007

LL mypow(LL a, LL n) {
    if(n == 0) return 1;
    if(n == 1) return a % MOD;
    if(n % 2 == 1) return (a * mypow(a, n-1)) % MOD;
    LL t = mypow(a, n/2);
    return (t * t) % MOD; 
}

LL mycomb(LL n, LL k) {
    if(n == 0 || n == k) return 1;
    LL x = 1, y = 1;
    REP(i, k) {
        x = x * (n-i) % MOD;
        y = y * (i+1) % MOD;
    }
    return x * mypow(y, MOD - 2) % MOD;
}

#define INF 1e8

struct edge {int u, v, cost;};

vector<edge> g;
VI par, rnk;

int root(int x) {
    if(par[x] == x) return x;
    else return par[x] = root(par[x]);
}

int same(int x, int y) {
    x = root(x);
    y = root(y);
    return x == y;
}

void unite(int x, int y) {
    x = root(x);
    y = root(y);
    if(rnk[x] > rnk[y]) {
        par[y] = x;
    } else {
        par[x] = y;
        if(rnk[x] == rnk[y]) rnk[y]++;
    }
}

struct node {int val; char c; node *l, *r;};

map<char, int> m, cnt;

void dfs(node *nd, int depth) {
    if(nd == NULL) return;
    // cerr << nd->val << endl;
    if(m[nd->c]) cnt[nd->c] = depth;
    dfs(nd->l, depth+1);
    dfs(nd->r, depth+1);
}

void printnode(node *nd) {
    if(nd == NULL) return;
    cerr << nd->val << ", " << nd->c << ", " << nd->l << ", " << nd->r << endl;
    printnode(nd->l);
    printnode(nd->r);
}

int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    string s;
    cin >> s;
    REP(i, s.size()) m[s[i]]++;
    // for(auto p : m) cerr << p.first << ", " << p.second << endl;
    auto cmp = [](node *x, node *y) {
        return x->val > y->val;
    };
    priority_queue<node*, vector<node*>, decltype(cmp)> q{cmp};
    node *head;
    for(auto p : m) {
        node *nd = (node*)malloc(sizeof(node));
        nd->val = p.second;
        nd->c = p.first;
        nd->l = NULL;
        nd->r = NULL;
        q.push(nd);
    }
    while(q.size() > 1) {
        // cerr << q.size() << endl;
        auto n1 = q.top(); q.pop();
        auto n2 = q.top(); q.pop();
        node *n3 = (node*)malloc(sizeof(node));
        n3->val = n1->val + n2->val;
        n3->c = '-';
        n3->l = n1;
        n3->r = n2;
        q.push(n3);
        head = n3;
    }
    // printnode(head);
    if(head->c != '-') {
        cout << s.size() << endl;
        return 0;
    }
    dfs(head, 0);
    // for(auto p : cnt) cerr << p.first << ", " << p.second << endl;
    int ans = 0;
    REP(i, s.size()) {
        ans += cnt[s[i]];
    }
    cout << ans << endl;
}
