#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <algorithm>
#include <ctype.h>

using namespace std;

const static int LLEN=1024;

void printACRONYM(char *line)
{
    string s; 
    istringstream lineIn(line);
    while (lineIn>>s)
    {
	cout << (const char) toupper(s[0]);
    }
}

int minValves(const vector<int> &b, int avg)
{
    int n=b.size();

    // base cases 
    if (n<=1) return 0;
    if (n==2) { if (b[0]==b[1]) return 0; else return 1; }

    vector<int> b2(b);  // copy constructor

    if (b2[n-1]==avg) { b2.pop_back(); return minValves(b2, avg); }

    if (b2[n-1]<avg) 
    { 
      b2[n-2] = b2[n-2] - (avg - b2[n-1]);
      b2.pop_back(); 
      return 1 + minValves(b2, avg); 
    }

    if (b2[n-1]>avg) 
    { 
      b2[n-2] = b2[n-2] + (b2[n-1]-avg);
      b2.pop_back(); 
      return 1 + minValves(b2, avg); 
    }

    return 1;
}

int main()
{
  vector<int> basins;

  while (1)
  {
    char line[LLEN];
    cin.getline(line, LLEN);
    if (line[0]=='#') return 0;
    printACRONYM(line);

    cin.getline(line, LLEN);    
    istringstream lineIn(line);

    int sum = 0;
    basins.resize(0);
    int v; while (lineIn>>v)
    { 
       basins.push_back(v);
       sum += v;
    }

    int n = basins.size();
    int i; for (i=0; i<n; i++) basins[i] = basins[i]*n; // normalize

    int min = n;
    for (i=0; i<n; i++)
    {
        int cnt = minValves(basins, sum);  // sum = avg of normalized list
	if (cnt < min) min = cnt;
	rotate(basins.begin(), basins.begin()+1, basins.end());
    }
    cout << ": " << min << "\n";
  }
}