#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;
namespace {
const int MOD107 = 1000000007;
const int MOD998 = 998244353;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <class T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
struct Modular {
 private:
  long long MODVALUE = 0;
  long long val = 0;
  Modular initModular(long long val) const { return Modular(val, MODVALUE); }
  inline void validate() const {}
  inline void validate(const Modular& other) const {}

 public:
  explicit operator long long() const { return val; }
  template <class T>
  Modular& operator=(const T& other) {
    val = (other % MODVALUE + MODVALUE) % MODVALUE;
    return *this;
  }
  long long getMod() { return MODVALUE; }
  template <class T>
  void setMod(const T& MOD) {
    MODVALUE = MOD;
  }
  bool operator==(const Modular& other) const {
    validate(other);
    return val == other.val;
  }
  bool operator!=(const Modular& other) const { return !(*this == other); }
  Modular& operator+=(const Modular& other) {
    validate(other);
    val += other.val;
    if (val >= MODVALUE) val -= MODVALUE;
    return *this;
  }
  Modular operator+(const Modular& other) const {
    Modular tmp = *this;
    return tmp += other;
  }
  template <class T>
  Modular& operator+=(const T& other) {
    return *this += initModular(other);
  }
  template <class T>
  Modular operator+(const T& other) const {
    return *this + initModular(other);
  }
  template <class T>
  friend Modular operator+(const T& other, const Modular& m) {
    return m.initModular(other) + m;
  }
  Modular& operator++() { return *this += 1; }
  Modular operator++(int) {
    Modular tmp = *this;
    ++*this;
    return tmp;
  }
  Modular operator-() const { return initModular(-val); }
  Modular& operator-=(const Modular& other) {
    validate(other);
    val -= other.val;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator-(const Modular& other) const {
    Modular tmp = *this;
    return tmp -= other;
  }
  template <class T>
  Modular& operator-=(const T& other) {
    return *this -= initModular(other);
  }
  template <class T>
  Modular operator-(const T& other) const {
    return *this - initModular(other);
  }
  template <class T>
  friend Modular operator-(const T& other, const Modular& m) {
    return m.initModular(other) - m;
  }
  Modular& operator--() { return *this -= 1; }
  Modular operator--(int) {
    Modular tmp = *this;
    --*this;
    return tmp;
  }
  Modular& operator*=(const Modular& other) {
    validate(other);
    val *= other.val;
    val %= MODVALUE;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator*(const Modular& other) const {
    Modular tmp = *this;
    return tmp *= other;
  }
  template <class T>
  Modular& operator*=(const T& other) {
    return *this *= initModular(other);
  }
  template <class T>
  Modular operator*(const T& other) const {
    return *this * initModular(other);
  }
  template <class T>
  friend Modular operator*(const T& other, const Modular& m) {
    return m.initModular(other) * m;
  }
  Modular pow(long long power) const {
    Modular m = *this, ans = initModular(1);
    while (power) {
      if (power & 1) ans *= m;
      m *= m;
      power >>= 1;
    }
    return ans;
  }
  Modular pow(const Modular& other) const { return pow(other.val); }
  Modular inv() const { return pow(MODVALUE - 2); }
  Modular& operator/=(const Modular& other) {
    val *= other.inv().val;
    val %= MODVALUE;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator/(const Modular& other) const {
    Modular tmp = *this;
    return tmp /= other;
  }
  template <class T>
  Modular& operator/=(const T& other) {
    return *this /= initModular(other);
  }
  template <class T>
  Modular operator/(const T& other) const {
    return *this / initModular(other);
  }
  template <class T>
  friend Modular operator/(const T& other, const Modular& m) {
    return m.initModular(other) / m;
  }
  friend istream& operator>>(istream& in, Modular& m) {
    in >> m.val;
    m.val %= m.MODVALUE;
    if (m.val < 0) m.val += m.MODVALUE;
    return in;
  }
  friend ostream& operator<<(ostream& out, const Modular& m) {
    return out << m.val;
  }
  Modular() {
    val = 0;
    MODVALUE = 0;
  }
  Modular(long long val, long long MOD)
      : MODVALUE(MOD), val((val % MOD + MOD) % MOD) {}
};
using Mint = Modular;
inline ll binpow(ll b, ll p, ll mod) {
  b %= mod;
  ll ans = 1;
  for (; p > 0; p >>= 1) {
    if (p & 1) {
      ans *= b;
      ans %= mod;
    }
    b *= b;
    b %= mod;
  }
  return ans;
}
inline ll max(ll a, int b) { return (a > b ? a : b); }
inline ll max(int a, ll b) { return (a > b ? a : b); }
inline ll min(ll a, int b) { return (a < b ? a : b); }
inline ll min(int a, ll b) { return (a < b ? a : b); }
template <class T>
inline bool chkmin(T& x, const T& y) {
  return y < x ? x = y, 1 : 0;
}
template <class T>
inline bool chkmax(T& x, const T& y) {
  return x < y ? x = y, 1 : 0;
}
}  // namespace
namespace IO {
struct InputWrapper {
 private:
  istream& in;

 public:
  template <class T>
  inline void _R(T& x) {
    in >> x;
  }
  template <class T1, class T2>
  inline void _R(pair<T1, T2>& x) {
    _R(x.first);
    _R(x.second);
  }
  template <class T>
  inline void _R(vector<T>& x) {
    for (auto& i : x) _R(i);
  }
  template <class T>
  inline void _R(deque<T>& x) {
    for (auto& i : x) _R(i);
  }
  inline void R() {}
  template <class T1, class... T2>
  inline void R(T1& x, T2&... y) {
    _R(x);
    R(y...);
  }
  template <class... T>
  inline void operator()(T&... x) {
    R(x...);
  }
  InputWrapper(istream& in) : in(in) {}
} R(cin);
struct OutputWrapper {
 private:
  ostream& out;

 public:
  template <class Container>
  inline void printContainer(const Container& x) {
    bool isFirst = 1;
    for (auto i : x) {
      if (!isFirst) out << ' ';
      isFirst = 0;
      _W(i);
    }
  }
  template <class T>
  inline void _W(const T& x) {
    out << x;
  }
  template <class T1, class T2>
  inline void _W(const pair<T1, T2>& p) {
    _W(p.first);
    _W(' ');
    _W(p.second);
  }
  template <class... T>
  inline void _W(const vector<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const deque<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const forward_list<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const list<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const set<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const multiset<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_set<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_multiset<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const map<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const multimap<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_map<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_multimap<T...>& x) {
    printContainer(x);
  }
  inline void W() { out << '\n'; }
  template <class T>
  inline void W(const T& x) {
    _W(x);
    W();
  }
  template <class T1, class... T2>
  inline void W(const T1& x, const T2&... y) {
    _W(x);
    _W(' ');
    W(y...);
  }
  template <class... T>
  inline void operator()(const T&... x) {
    W(x...);
  }
  OutputWrapper(ostream& out) : out(out) {}
} W(cout), D(cerr);
}  // namespace IO
using namespace IO;
namespace outputFormat {
inline string Case(int tc) { return "Case #" + to_string(tc) + ':'; }
inline string YN(bool b) { return b ? "Yes" : "No"; }
}  // namespace outputFormat
using namespace outputFormat;
namespace std {
template <class T1, class T2>
struct hash<pair<T1, T2>> {
  std::size_t operator()(pair<T1, T2> _) const {
    return hash<T1>{}(_.first) ^ hash<T2>{}(_.second);
  }
};
}  // namespace std
int main() {
  int t;
  cin >> t;
  while (t--) {
    string s;
    R(s);
    const int n = s.length();
    vector<int> zp;
    for (int i = 0; i < n; i++)
      if (s[i] == '0') zp.emplace_back(i);
    if (zp.empty()) {
      W(0);
    } else if (zp.back() - zp.front() + 1 == (int)zp.size()) {
      W(1);
    } else {
      W(2);
    }
  }
  return 0;
}
static auto __init__ = []() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  return 42;
}();

### Prompt

Your task is to create a cpp solution to the following problem:

A binary string is a string that consists of characters 0 and 1.

Let \operatorname{MEX} of a binary string be the smallest digit among 0, 1, or 2 that does not occur in the string. For example, \operatorname{MEX} of 001011 is 2, because 0 and 1 occur in the string at least once, \operatorname{MEX} of 1111 is 0, because 0 and 2 do not occur in the string and 0 < 2.

A binary string s is given. You should cut it into any number of substrings such that each character is in exactly one substring. It is possible to cut the string into a single substring — the whole string.

A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

What is the minimal sum of \operatorname{MEX} of all substrings pieces can be?

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

Each test case contains a single binary string s (1 ≤ |s| ≤ 10^5).

It's guaranteed that the sum of lengths of s over all test cases does not exceed 10^5.

Output

For each test case print a single integer — the minimal sum of \operatorname{MEX} of all substrings that it is possible to get by cutting s optimally.

Example

Input


6
01
1111
01100
101
0000
01010


Output


1
0
2
1
1
2

Note

In the first test case the minimal sum is \operatorname{MEX}(0) + \operatorname{MEX}(1) = 1 + 0 = 1.

In the second test case the minimal sum is \operatorname{MEX}(1111) = 0.

In the third test case the minimal sum is \operatorname{MEX}(01100) = 2.

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;
namespace {
const int MOD107 = 1000000007;
const int MOD998 = 998244353;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <class T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
struct Modular {
 private:
  long long MODVALUE = 0;
  long long val = 0;
  Modular initModular(long long val) const { return Modular(val, MODVALUE); }
  inline void validate() const {}
  inline void validate(const Modular& other) const {}

 public:
  explicit operator long long() const { return val; }
  template <class T>
  Modular& operator=(const T& other) {
    val = (other % MODVALUE + MODVALUE) % MODVALUE;
    return *this;
  }
  long long getMod() { return MODVALUE; }
  template <class T>
  void setMod(const T& MOD) {
    MODVALUE = MOD;
  }
  bool operator==(const Modular& other) const {
    validate(other);
    return val == other.val;
  }
  bool operator!=(const Modular& other) const { return !(*this == other); }
  Modular& operator+=(const Modular& other) {
    validate(other);
    val += other.val;
    if (val >= MODVALUE) val -= MODVALUE;
    return *this;
  }
  Modular operator+(const Modular& other) const {
    Modular tmp = *this;
    return tmp += other;
  }
  template <class T>
  Modular& operator+=(const T& other) {
    return *this += initModular(other);
  }
  template <class T>
  Modular operator+(const T& other) const {
    return *this + initModular(other);
  }
  template <class T>
  friend Modular operator+(const T& other, const Modular& m) {
    return m.initModular(other) + m;
  }
  Modular& operator++() { return *this += 1; }
  Modular operator++(int) {
    Modular tmp = *this;
    ++*this;
    return tmp;
  }
  Modular operator-() const { return initModular(-val); }
  Modular& operator-=(const Modular& other) {
    validate(other);
    val -= other.val;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator-(const Modular& other) const {
    Modular tmp = *this;
    return tmp -= other;
  }
  template <class T>
  Modular& operator-=(const T& other) {
    return *this -= initModular(other);
  }
  template <class T>
  Modular operator-(const T& other) const {
    return *this - initModular(other);
  }
  template <class T>
  friend Modular operator-(const T& other, const Modular& m) {
    return m.initModular(other) - m;
  }
  Modular& operator--() { return *this -= 1; }
  Modular operator--(int) {
    Modular tmp = *this;
    --*this;
    return tmp;
  }
  Modular& operator*=(const Modular& other) {
    validate(other);
    val *= other.val;
    val %= MODVALUE;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator*(const Modular& other) const {
    Modular tmp = *this;
    return tmp *= other;
  }
  template <class T>
  Modular& operator*=(const T& other) {
    return *this *= initModular(other);
  }
  template <class T>
  Modular operator*(const T& other) const {
    return *this * initModular(other);
  }
  template <class T>
  friend Modular operator*(const T& other, const Modular& m) {
    return m.initModular(other) * m;
  }
  Modular pow(long long power) const {
    Modular m = *this, ans = initModular(1);
    while (power) {
      if (power & 1) ans *= m;
      m *= m;
      power >>= 1;
    }
    return ans;
  }
  Modular pow(const Modular& other) const { return pow(other.val); }
  Modular inv() const { return pow(MODVALUE - 2); }
  Modular& operator/=(const Modular& other) {
    val *= other.inv().val;
    val %= MODVALUE;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator/(const Modular& other) const {
    Modular tmp = *this;
    return tmp /= other;
  }
  template <class T>
  Modular& operator/=(const T& other) {
    return *this /= initModular(other);
  }
  template <class T>
  Modular operator/(const T& other) const {
    return *this / initModular(other);
  }
  template <class T>
  friend Modular operator/(const T& other, const Modular& m) {
    return m.initModular(other) / m;
  }
  friend istream& operator>>(istream& in, Modular& m) {
    in >> m.val;
    m.val %= m.MODVALUE;
    if (m.val < 0) m.val += m.MODVALUE;
    return in;
  }
  friend ostream& operator<<(ostream& out, const Modular& m) {
    return out << m.val;
  }
  Modular() {
    val = 0;
    MODVALUE = 0;
  }
  Modular(long long val, long long MOD)
      : MODVALUE(MOD), val((val % MOD + MOD) % MOD) {}
};
using Mint = Modular;
inline ll binpow(ll b, ll p, ll mod) {
  b %= mod;
  ll ans = 1;
  for (; p > 0; p >>= 1) {
    if (p & 1) {
      ans *= b;
      ans %= mod;
    }
    b *= b;
    b %= mod;
  }
  return ans;
}
inline ll max(ll a, int b) { return (a > b ? a : b); }
inline ll max(int a, ll b) { return (a > b ? a : b); }
inline ll min(ll a, int b) { return (a < b ? a : b); }
inline ll min(int a, ll b) { return (a < b ? a : b); }
template <class T>
inline bool chkmin(T& x, const T& y) {
  return y < x ? x = y, 1 : 0;
}
template <class T>
inline bool chkmax(T& x, const T& y) {
  return x < y ? x = y, 1 : 0;
}
}  // namespace
namespace IO {
struct InputWrapper {
 private:
  istream& in;

 public:
  template <class T>
  inline void _R(T& x) {
    in >> x;
  }
  template <class T1, class T2>
  inline void _R(pair<T1, T2>& x) {
    _R(x.first);
    _R(x.second);
  }
  template <class T>
  inline void _R(vector<T>& x) {
    for (auto& i : x) _R(i);
  }
  template <class T>
  inline void _R(deque<T>& x) {
    for (auto& i : x) _R(i);
  }
  inline void R() {}
  template <class T1, class... T2>
  inline void R(T1& x, T2&... y) {
    _R(x);
    R(y...);
  }
  template <class... T>
  inline void operator()(T&... x) {
    R(x...);
  }
  InputWrapper(istream& in) : in(in) {}
} R(cin);
struct OutputWrapper {
 private:
  ostream& out;

 public:
  template <class Container>
  inline void printContainer(const Container& x) {
    bool isFirst = 1;
    for (auto i : x) {
      if (!isFirst) out << ' ';
      isFirst = 0;
      _W(i);
    }
  }
  template <class T>
  inline void _W(const T& x) {
    out << x;
  }
  template <class T1, class T2>
  inline void _W(const pair<T1, T2>& p) {
    _W(p.first);
    _W(' ');
    _W(p.second);
  }
  template <class... T>
  inline void _W(const vector<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const deque<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const forward_list<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const list<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const set<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const multiset<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_set<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_multiset<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const map<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const multimap<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_map<T...>& x) {
    printContainer(x);
  }
  template <class... T>
  inline void _W(const unordered_multimap<T...>& x) {
    printContainer(x);
  }
  inline void W() { out << '\n'; }
  template <class T>
  inline void W(const T& x) {
    _W(x);
    W();
  }
  template <class T1, class... T2>
  inline void W(const T1& x, const T2&... y) {
    _W(x);
    _W(' ');
    W(y...);
  }
  template <class... T>
  inline void operator()(const T&... x) {
    W(x...);
  }
  OutputWrapper(ostream& out) : out(out) {}
} W(cout), D(cerr);
}  // namespace IO
using namespace IO;
namespace outputFormat {
inline string Case(int tc) { return "Case #" + to_string(tc) + ':'; }
inline string YN(bool b) { return b ? "Yes" : "No"; }
}  // namespace outputFormat
using namespace outputFormat;
namespace std {
template <class T1, class T2>
struct hash<pair<T1, T2>> {
  std::size_t operator()(pair<T1, T2> _) const {
    return hash<T1>{}(_.first) ^ hash<T2>{}(_.second);
  }
};
}  // namespace std
int main() {
  int t;
  cin >> t;
  while (t--) {
    string s;
    R(s);
    const int n = s.length();
    vector<int> zp;
    for (int i = 0; i < n; i++)
      if (s[i] == '0') zp.emplace_back(i);
    if (zp.empty()) {
      W(0);
    } else if (zp.back() - zp.front() + 1 == (int)zp.size()) {
      W(1);
    } else {
      W(2);
    }
  }
  return 0;
}
static auto __init__ = []() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  return 42;
}();

```