#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

#define forn(i, n) for (int i = 0; i < n; i++)

typedef long long ll;

const int maxN = 250000;

int n, num[maxN + 1];
char s[maxN + 1];
int p[maxN], col[maxN], p2[maxN], len[maxN];

void BuildArray()
{
  int ma = max(n, 256);
  forn(i, n)
    col[i] = s[i], p[i] = i;

  for (int k2 = 1; k2 / 2 < n; k2 *= 2)
  {
    int k = k2 / 2;
    memset(num, 0, sizeof(num));
    forn(i, n)
      num[col[i] + 1]++;
    forn(i, ma)
      num[i + 1] += num[i];
    forn(i, n)
      p2[num[col[(p[i] - k + n) % n]]++] = (p[i] - k + n) % n;

    int cc = 0;
    forn(i, n)
    {
      if (i && (col[p2[i]] != col[p2[i - 1]] || col[(p2[i] + k) % n] != col[(p2[i - 1] + k) % n]))
        cc++;
      num[p2[i]] = cc;
    }
    forn(i, n)
      p[i] = p2[i], col[i] = num[i];
  }
 
  // make it stable
  memset(num, 0, sizeof(num));
  forn(i, n)
    num[col[i] + 1]++;
  forn(i, ma)
    num[i + 1] += num[i];
  forn(i, n)
    p2[num[col[i]]++] = i;
  forn(i, n)
    p[i] = p2[i];

  // calc inverse permutation
  forn(i, n)
    p2[p[i]] = i;
}

void BuildLCP()
{
  int lcp = 0;
  forn(i, n)
  {
    int j = p2[i];
    lcp = max(0, lcp - 1);
    if (j != n - 1)
      while (lcp < n && s[(p[j] + lcp) % n] == s[(p[j + 1] + lcp) % n])
        lcp++;
    len[j] = lcp;
    if (j != n - 1 && p[j + 1] == n - 1)
      lcp = 0;
  }
}

int main()
{
  scanf("%d%s", &n, s);

  BuildArray();
  BuildLCP();

  // res = sum of all LCP[i,i+1]
  ll res = 0;
  forn(i, n)
    res += len[i];
  printf("%.3f\n", (double)res / (n - 1));
  return 0;
}
