Problem: Once Petya read a problem about a bracket sequence. He gave it much thought but didn't find a solution. Today you will face it.

You are given string s. It represents a correct bracket sequence. A correct bracket sequence is the sequence of opening ("(") and closing (")") brackets, such that it is possible to obtain a correct mathematical expression from it, inserting numbers and operators between the brackets. For example, such sequences as "(())()" and "()" are correct bracket sequences and such sequences as ")()" and "(()" are not.

In a correct bracket sequence each bracket corresponds to the matching bracket (an opening bracket corresponds to the matching closing bracket and vice versa). For example, in a bracket sequence shown of the figure below, the third bracket corresponds to the matching sixth one and the fifth bracket corresponds to the fourth one.

<image>

You are allowed to color some brackets in the bracket sequence so as all three conditions are fulfilled: 

  * Each bracket is either not colored any color, or is colored red, or is colored blue. 
  * For any pair of matching brackets exactly one of them is colored. In other words, for any bracket the following is true: either it or the matching bracket that corresponds to it is colored. 
  * No two neighboring colored brackets have the same color. 



Find the number of different ways to color the bracket sequence. The ways should meet the above-given conditions. Two ways of coloring are considered different if they differ in the color of at least one bracket. As the result can be quite large, print it modulo 1000000007 (109 + 7).

Input

The first line contains the single string s (2 ≤ |s| ≤ 700) which represents a correct bracket sequence. 

Output

Print the only number — the number of ways to color the bracket sequence that meet the above given conditions modulo 1000000007 (109 + 7).

Examples

Input

(())


Output

12


Input

(()())


Output

40


Input

()


Output

4

Note

Let's consider the first sample test. The bracket sequence from the sample can be colored, for example, as is shown on two figures below. 

<image> <image>

The two ways of coloring shown below are incorrect. 

<image> <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
using namespace std;
const double inf = 1e121;
const double eps = 1e-10;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int randint(int l, int r) {
  int out = rng() % (r - l + 1) + l;
  return out >= l ? out : out + r - l + 1;
}
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ",";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ",";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + "," + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + "," + to_string(get<1>(p)) + "," +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + "," + to_string(get<1>(p)) + "," +
         to_string(get<2>(p)) + "," + to_string(get<3>(p)) + ")";
}
template <typename A, typename B, typename C, typename D, typename E>
string to_string(tuple<A, B, C, D, E> p) {
  return "(" + to_string(get<0>(p)) + "," + to_string(get<1>(p)) + "," +
         to_string(get<2>(p)) + "," + to_string(get<3>(p)) + "," +
         to_string(get<4>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T>
struct is_pair {
  static const bool value = false;
};
template <typename T, typename U>
struct is_pair<std::pair<T, U>> {
  static const bool value = true;
};
const int INF = 0x3f3f3f3f;
template <typename T>
typename enable_if<!is_integral<T>::value && !is_pair<T>::value, void>::type
read(T& x) {
  cin >> x;
}
long long read() {
  char c;
  long long out = 0, f = 1;
  for (c = getchar(); !isdigit(c) && c != '-'; c = getchar())
    ;
  if (c == '-') {
    f = -1;
    c = getchar();
  }
  for (; isdigit(c); c = getchar()) out = (out << 3) + (out << 1) + c - '0';
  return out * f;
}
template <typename T>
typename enable_if<is_integral<T>::value, T>::type read(T& x) {
  char c;
  T f = 1;
  x = 0;
  for (c = getchar(); !isdigit(c) && c != '-'; c = getchar())
    ;
  if (c == '-') {
    f = -1;
    c = getchar();
  }
  for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
  return x *= f;
}
char read(char& x) {
  for (x = getchar(); isspace(x); x = getchar())
    ;
  return x;
}
double read(double& x) {
  scanf("%lf", &x);
  return x;
}
long double read(long double& x) {
  scanf("%Lf", &x);
  return x;
}
template <typename T>
typename enable_if<!is_integral<T>::value && !is_pair<T>::value, void>::type
write(const T& x) {
  cout << x;
}
template <typename T>
typename enable_if<is_integral<T>::value, void>::type write(const T& x) {
  if (x < 0) {
    putchar('-');
    write(-x);
    return;
  }
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
void write(const char& x) { putchar(x); }
void write(const double& x) { printf("%.10lf", x); }
void write(const long double& x) { printf("%.10Lf", x); }
template <typename T>
typename enable_if<is_pair<T>::value, void>::type read(T& x) {
  read(x.first);
  read(x.second);
}
template <typename T>
typename enable_if<is_pair<T>::value, void>::type write(const T& x) {
  write(x.first);
  putchar(' ');
  write(x.second);
}
template <typename T, typename... Args>
void read(T& x, Args&... args) {
  read(x);
  read(args...);
}
template <
    typename OutputIt,
    typename = typename enable_if<
        is_same<output_iterator_tag,
                typename iterator_traits<OutputIt>::iterator_category>::value ||
        (is_base_of<forward_iterator_tag, typename iterator_traits<OutputIt>::
                                              iterator_category>::value &&
         !is_const<OutputIt>::value)>::type>
void read(OutputIt __first, OutputIt __last) {
  for (; __first != __last; ++__first) read(*__first);
}
template <
    typename InputIt,
    typename = typename enable_if<is_base_of<
        input_iterator_tag,
        typename iterator_traits<InputIt>::iterator_category>::value>::type>
void wts(InputIt __first, InputIt __last) {
  bool isFirst = true;
  for (; __first != __last; ++__first) {
    if (isFirst)
      isFirst = false;
    else
      putchar(' ');
    write(*__first);
  }
  putchar('\n');
}
template <
    typename InputIt,
    typename = typename enable_if<is_base_of<
        input_iterator_tag,
        typename iterator_traits<InputIt>::iterator_category>::value>::type>
void wtb(InputIt __first, InputIt __last) {
  for (; __first != __last; ++__first) {
    write(*__first);
    putchar('\n');
  }
}
template <typename T>
void wts(const T& x) {
  write(x);
  putchar(' ');
}
template <typename T>
void wtb(const T& x) {
  write(x);
  putchar('\n');
}
template <typename T>
void wte(const T& x) {
  write(x);
  exit(0);
}
template <typename T, typename... Args>
void wts(const T& x, Args... args) {
  wts(x);
  wts(args...);
}
template <typename T, typename... Args>
void wtb(const T& x, Args... args) {
  wts(x);
  wtb(args...);
}
template <typename T, typename... Args>
void wte(const T& x, Args... args) {
  wts(x);
  wte(args...);
}
template <typename T1, typename T2>
inline bool up(T1& x, const T2& y) {
  return x < y ? x = y, 1 : 0;
}
template <typename T1, typename T2>
inline bool dn(T1& x, const T2& y) {
  return y < x ? x = y, 1 : 0;
}
template <typename T>
inline bool inRange(const T& x, const T& l, const T& r) {
  return !(x < l) && !(r < x);
}
template <typename T1, typename T2>
inline auto minOfDifferentTypes(const T1& x, const T2& y)
    -> decltype(x < y ? x : y) {
  return x < y ? x : y;
}
template <typename T1, typename T2>
inline auto maxOfDifferentTypes(const T1& x, const T2& y)
    -> decltype(x < y ? y : x) {
  return x < y ? y : x;
}
const int mod = 1e9 + 7;
int modadd(int x, int y) { return (x += y) >= mod ? x - mod : x; }
signed main() {
  string s;
  read(s);
  int n = s.size();
  vector<vector<vector<vector<int>>>> f(
      n, vector<vector<vector<int>>>(
             n, vector<vector<int>>(6, vector<int>(6, 0))));
  for (int i = (0), iend = (n - 2); i <= iend; ++i)
    f[i + 1][i] = vector<vector<int>>(6, vector<int>(6, 1));
  for (int len = (2), lenend = (n); len <= lenend; ++len) {
    for (int l = (0), lend = (n - len); l <= lend; ++l) {
      int r = l + len - 1, cnt = 0;
      int p = -1;
      for (int i = (l), iend = (r); i <= iend; ++i) {
        cnt += s[i] == '(' ? 1 : -1;
        if (cnt < 0) break;
        if (cnt == 0 && p == -1) p = i;
      }
      if (cnt == 0) {
        for (int i = (0), iend = (5); i <= iend; ++i) {
          for (int j = (0), jend = (5); j <= jend; ++j) {
            for (int lc = (0), lcend = (2); lc <= lcend; ++lc) {
              if (i < 3 && lc != i) continue;
              if (i > 3 && lc == i - 3) continue;
              for (int rc = (0), rcend = (2); rc <= rcend; ++rc) {
                if (j < 3 && rc != j) continue;
                if (j > 3 && rc == j - 3) continue;
                if ((!lc || !rc) && (lc || rc))
                  f[l][r][i][j] =
                      modadd(f[l][r][i][j], f[l + 1][r - 1][lc + 3][rc + 3]);
                if (~p && p < r) {
                  for (int x = (0), xend = (2); x <= xend; ++x) {
                    for (int y = (0), yend = (2); y <= yend; ++y) {
                      if (!x || x != y)
                        f[l][r][i][j] =
                            modadd(f[l][r][i][j], (long long)f[l][p][lc][x] *
                                                      f[p + 1][r][y][rc] % mod);
                    }
                  }
                }
              }
            }
            42;
          }
        }
      }
    }
  }
  wtb(f[0][n - 1][3][3]);
  return 0;
}