Problem: Dreamoon saw a large integer x written on the ground and wants to print its binary form out. Dreamoon has accomplished the part of turning x into its binary format. Now he is going to print it in the following manner.

He has an integer n = 0 and can only perform the following two operations in any order for unlimited times each:

  1. Print n in binary form without leading zeros, each print will append to the right of previous prints. 
  2. Increase n by 1. 



Let's define an ideal sequence as a sequence of operations that can successfully print binary representation of x without leading zeros and ends with a print operation (i.e. operation 1). Dreamoon wants to know how many different ideal sequences are there and the length (in operations) of the shortest ideal sequence.

The answers might be large so please print them modulo 1000000007 (109 + 7).

Let's define the string representation of an ideal sequence as a string of '1' and '2' where the i-th character in the string matches the i-th operation performed. Two ideal sequences are called different if their string representations are different.

Input

The single line of the input contains a binary integer representing x (1 ≤ x < 25000) without leading zeros.

Output

The first line of the output should contain an integer representing the number of different ideal sequences modulo 1000000007 (109 + 7).

The second line of the output contains an integer representing the minimal length of an ideal sequence modulo 1000000007 (109 + 7).

Examples

Input

101


Output

1
6


Input

11010


Output

3
5

Note

For the first sample, the shortest and the only ideal sequence is «222221» of length 6.

For the second sample, there are three ideal sequences «21211», «212222222221», «222222222222222222222222221». Among them the shortest one has length 5.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-6;
template <typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
  os << to_string(p.first) << " " << to_string(p.second);
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
  for (ll i = (0); i < (ll)(v.size()); i++) {
    if (i) os << " ";
    os << v[i];
  }
  return os;
}
struct modint {
  ll n;

 public:
  modint(const ll n = 0) : n((n % mod + mod) % mod) {}
  static modint pow(modint a, int m) {
    modint r = 1;
    while (m > 0) {
      if (m & 1) {
        r *= a;
      }
      a = (a * a);
      m /= 2;
    }
    return r;
  }
  modint& operator++() {
    *this += 1;
    return *this;
  }
  modint& operator--() {
    *this -= 1;
    return *this;
  }
  modint operator++(int) {
    modint ret = *this;
    *this += 1;
    return ret;
  }
  modint operator--(int) {
    modint ret = *this;
    *this -= 1;
    return ret;
  }
  modint operator~() const { return (this->pow(n, mod - 2)); }
  friend bool operator==(const modint& lhs, const modint& rhs) {
    return lhs.n == rhs.n;
  }
  friend bool operator<(const modint& lhs, const modint& rhs) {
    return lhs.n < rhs.n;
  }
  friend bool operator>(const modint& lhs, const modint& rhs) {
    return lhs.n > rhs.n;
  }
  friend modint& operator+=(modint& lhs, const modint& rhs) {
    lhs.n += rhs.n;
    if (lhs.n >= mod) lhs.n -= mod;
    return lhs;
  }
  friend modint& operator-=(modint& lhs, const modint& rhs) {
    lhs.n -= rhs.n;
    if (lhs.n < 0) lhs.n += mod;
    return lhs;
  }
  friend modint& operator*=(modint& lhs, const modint& rhs) {
    lhs.n = (lhs.n * rhs.n) % mod;
    return lhs;
  }
  friend modint& operator/=(modint& lhs, const modint& rhs) {
    lhs.n = (lhs.n * (~rhs).n) % mod;
    return lhs;
  }
  friend modint operator+(const modint& lhs, const modint& rhs) {
    return modint(lhs.n + rhs.n);
  }
  friend modint operator-(const modint& lhs, const modint& rhs) {
    return modint(lhs.n - rhs.n);
  }
  friend modint operator*(const modint& lhs, const modint& rhs) {
    return modint(lhs.n * rhs.n);
  }
  friend modint operator/(const modint& lhs, const modint& rhs) {
    return modint(lhs.n * (~rhs).n);
  }
};
istream& operator>>(istream& is, modint m) {
  is >> m.n;
  return is;
}
ostream& operator<<(ostream& os, modint m) {
  os << m.n;
  return os;
}
long long extgcd(long long a, long long b, long long& x, long long& y) {
  long long d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}
long long mod_inverse(long long a, long long m) {
  long long x, y;
  if (extgcd(a, m, x, y) == 1)
    return (m + x % m) % m;
  else
    return -1;
}
vector<long long> fact(1010101 + 1, inf);
long long mod_fact(long long n, long long& e) {
  if (fact[0] == inf) {
    fact[0] = 1;
    if (1010101 != 0) fact[1] = 1;
    for (ll i = 2; i <= 1010101; ++i) {
      fact[i] = (fact[i - 1] * i) % mod;
    }
  }
  e = 0;
  if (n == 0) return 1;
  long long res = mod_fact(n / mod, e);
  e += n / mod;
  if ((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
  return (res * fact[n % mod]) % mod;
}
long long mod_comb(long long n, long long k) {
  if (n < 0 || k < 0 || n < k) return 0;
  long long e1, e2, e3;
  long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2),
            a3 = mod_fact(n - k, e3);
  if (e1 > e2 + e3) return 0;
  return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}
using mi = modint;
mi mod_pow(mi a, ll n) {
  mi ret = 1;
  mi tmp = a;
  while (n > 0) {
    if (n % 2) ret *= tmp;
    tmp = tmp * tmp;
    n /= 2;
  }
  return ret;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
struct SuffixArray {
  vector<int> SA;
  const string s;
  SuffixArray(const string& str) : s(str) {
    SA.resize(s.size());
    iota(begin(SA), end(SA), 0);
    sort(begin(SA), end(SA),
         [&](int a, int b) { return s[a] == s[b] ? a > b : s[a] < s[b]; });
    vector<int> classes(s.size()), c(s.begin(), s.end()), cnt(s.size());
    for (int len = 1; len < s.size(); len <<= 1) {
      for (int i = 0; i < s.size(); i++) {
        if (i > 0 && c[SA[i - 1]] == c[SA[i]] && SA[i - 1] + len < s.size() &&
            c[SA[i - 1] + len / 2] == c[SA[i] + len / 2]) {
          classes[SA[i]] = classes[SA[i - 1]];
        } else {
          classes[SA[i]] = i;
        }
      }
      iota(begin(cnt), end(cnt), 0);
      copy(begin(SA), end(SA), begin(c));
      for (int i = 0; i < s.size(); i++) {
        int s1 = c[i] - len;
        if (s1 >= 0) SA[cnt[classes[s1]]++] = s1;
      }
      classes.swap(c);
    }
  }
  int operator[](int k) const { return SA[k]; }
  size_t size() const { return s.size(); }
  bool lt_substr(const string& t, int si = 0, int ti = 0) {
    int sn = (int)s.size(), tn = (int)t.size();
    while (si < sn && ti < tn) {
      if (s[si] < t[ti]) return true;
      if (s[si] > t[ti]) return false;
      ++si, ++ti;
    }
    return si >= sn && ti < tn;
  }
  int lower_bound(const string& t) {
    int low = -1, high = (int)SA.size();
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (lt_substr(t, SA[mid]))
        low = mid;
      else
        high = mid;
    }
    return high;
  }
  pair<int, int> lower_upper_bound(string& t) {
    int idx = lower_bound(t);
    int low = idx - 1, high = (int)SA.size();
    t.back()++;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (lt_substr(t, SA[mid]))
        low = mid;
      else
        high = mid;
    }
    t.back()--;
    return {idx, high};
  }
  void output() {
    for (int i = 0; i < size(); i++) {
      cout << i << ": " << s.substr(SA[i]) << endl;
    }
  }
};
struct LongestCommonPrefixArray {
  const SuffixArray& SA;
  vector<int> LCP, rank;
  LongestCommonPrefixArray(const SuffixArray& SA) : SA(SA), LCP(SA.size()) {
    rank.resize(SA.size());
    for (int i = 0; i < SA.size(); i++) {
      rank[SA[i]] = i;
    }
    for (int i = 0, h = 0; i < SA.size(); i++) {
      if (rank[i] + 1 < SA.size()) {
        for (int j = SA[rank[i] + 1];
             max(i, j) + h < SA.size() && SA.s[i + h] == SA.s[j + h]; ++h)
          ;
        LCP[rank[i] + 1] = h;
        if (h > 0) --h;
      }
    }
  }
  int operator[](int k) const { return LCP[k]; }
  size_t size() const { return LCP.size(); }
  void output() {
    for (int i = 0; i < size(); i++) {
      cout << i << ": " << LCP[i] << " " << SA.s.substr(SA[i]) << endl;
    }
  }
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  string x;
  cin >> x;
  int n = (int)x.size();
  SuffixArray sa(x);
  LongestCommonPrefixArray lcpa(sa);
  vector<vector<int>> pd(n, vector<int>(n));
  vector<int> rev(n);
  for (ll i = (0); i < (ll)(n); i++) rev[sa[i]] = i;
  for (ll i = (0); i < (ll)(n - 1); i++) {
    int a = sa[i];
    int mn = lcpa[i + 1];
    for (int j = i + 1; j < n; j++) {
      mn = min(mn, lcpa[j]);
      int b = sa[j];
      pd[a][b] = pd[b][a] = mn;
    }
  }
  vector<vector<pair<int, int>>> dp(
      n, vector<pair<int, int>>(n, make_pair(0, inf)));
  vector<vector<pair<int, int>>> acm(
      n, vector<pair<int, int>>(n, make_pair(0, inf)));
  for (ll i = (0); i < (ll)(n); i++) {
    for (ll j = (0); j < (ll)(n); j++) {
      if (i + 1 < j + 1) continue;
      if (x[i - j] == '0') continue;
      if (i + 1 == j + 1) {
        dp[i][j].first = 1;
        dp[i][j].second = 1;
      } else {
        if (j) {
          dp[i][j].first = acm[i - j - 1][j - 1].first;
          dp[i][j].second = acm[i - j - 1][j - 1].second + 1;
        }
        if (i - j - 1 - j < 0) continue;
        if (pd[i - j - 1 - j][i - j] >= j + 1) {
          dp[i][j].first += dp[i - j - 1][j].first;
          dp[i][j].first %= mod;
          dp[i][j].second = min(dp[i][j].second, dp[i - j - 1][j].second + 1);
        } else if (rev[i - j - 1 - j] < rev[i - j]) {
          dp[i][j].first += dp[i - j - 1][j].first;
          dp[i][j].first %= mod;
          dp[i][j].second = min(dp[i][j].second, dp[i - j - 1][j].second + 1);
        }
      }
    }
    acm[i][0] = dp[i][0];
    for (ll j = (1); j < (ll)(n); j++) {
      acm[i][j].first = acm[i][j - 1].first + dp[i][j].first;
      acm[i][j].first %= mod;
      acm[i][j].second = min(acm[i][j - 1].second, dp[i][j].second);
    }
  }
  mi ans1 = acm[n - 1][n - 1].first;
  ll ans2 = inf * inf;
  ll tmp = 0;
  bool good = false;
  for (int i = n - 1; i >= 0; i--) {
    if (x[i] == '1') tmp += mod_pow(2, n - 1 - i).n;
    if (good && n - 1 - i > 8) break;
    if (n - 1 - i > 8) tmp %= mod;
    if (acm[n - 1][n - 1 - i].second != inf) {
      good = true;
      if (n - 1 - i > 8) {
        ans2 = tmp + acm[n - 1][n - 1 - i].second;
        break;
      } else {
        ans2 = min(ans2, tmp + acm[n - 1][n - 1 - i].second);
      }
    }
  }
  ans2 %= mod;
  cout << ans1 << endl;
  cout << ans2 << endl;
  return 0;
}