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>
using std::cin;
using std::cout;
using std::endl;
using std::ifstream;
using std::make_pair;
using std::max;
using std::min;
using std::ofstream;
using std::pair;
using std::stack;
using std::string;
using std::stringstream;
using std::vector;
class ColBracket149D {
 public:
  ColBracket149D();
  ~ColBracket149D();
  void input();
  void output();
  long long mod_add(long long a, long long b);
  long long mod_mult(long long a, long long b);
  void TreeDpHelper(string str, vector<long long> index_vec, long long start,
                    long long end, long long depth = 0);
  long long Dynamic(string str);
  vector<long long> ParenMatch(string str);
  bool checkCompatible(long long pre, long long cur);
  long long getDpValue(long long curr_dp, vector<long long> seg_vec);

 private:
  bool debug_flag;
  bool debug_flag2;
  static long long dp[702][5];
  static long long sumdp[702][5];
  string input_str_;
};
ColBracket149D::ColBracket149D() {
  debug_flag = false;
  debug_flag2 = false;
};
ColBracket149D::~ColBracket149D(){};
long long ColBracket149D::dp[702][5];
long long ColBracket149D::sumdp[702][5];
void ColBracket149D::input() { cin >> input_str_; }
void ColBracket149D::output() {
  long long output_res = Dynamic(input_str_);
  cout << output_res << endl;
}
long long ColBracket149D::mod_add(long long a, long long b) {
  long long mod_mask = 1000000007;
  a %= mod_mask;
  b %= mod_mask;
  long long sum = a + b;
  return sum % mod_mask;
}
long long ColBracket149D::mod_mult(long long a, long long b) {
  long long mod_mask = 1000000007;
  a %= mod_mask;
  b %= mod_mask;
  long long mul = a * b;
  return mul % mod_mask;
}
vector<long long> ColBracket149D::ParenMatch(string str) {
  long long str_len = str.size();
  stack<long long> stack;
  vector<long long> index_vec;
  index_vec.resize(str_len);
  for (long long str_i = 0; str_i < str_len; ++str_i) {
    if (str[str_i] == '(') {
      stack.push(str_i);
    } else {
      long long top_index = stack.top();
      index_vec[str_i] = top_index;
      index_vec[top_index] = str_i;
      stack.pop();
    }
  }
  return index_vec;
}
bool ColBracket149D::checkCompatible(long long pre, long long curr) {
  return !(pre == 2 && curr == 0) && !(pre == 3 && curr == 1);
}
long long ColBracket149D::getDpValue(long long curr_dp,
                                     vector<long long> seg_vec) {
  memset(sumdp, 0, sizeof(sumdp));
  long long sum = 0;
  long long start, pre_start;
  if (curr_dp < 2) {
    for (long long vec_i = 0; vec_i < (long long)(seg_vec.size()); ++vec_i) {
      start = seg_vec[vec_i];
      if (vec_i == 0) {
        for (long long dp_i = 0; dp_i < 4; ++dp_i) {
          if (dp_i == curr_dp) {
            sumdp[vec_i][dp_i] = 0;
          } else {
            sumdp[vec_i][dp_i] = dp[start][dp_i];
          }
        }
      } else {
        for (long long dp_i = 0; dp_i < 4; ++dp_i) {
          long long pre_sum = 0;
          for (long long pre_dp_i = 0; pre_dp_i < 4; ++pre_dp_i) {
            if (checkCompatible(pre_dp_i, dp_i)) {
              pre_sum = mod_add(pre_sum, sumdp[vec_i - 1][pre_dp_i]);
            }
          }
          pre_sum = mod_mult(pre_sum, dp[start][dp_i]);
          sumdp[vec_i][dp_i] = pre_sum;
        }
      }
      pre_start = start;
    }
    sum = 0;
    long long vec_i = (long long)(seg_vec.size() - 1);
    for (long long dp_i = 0; dp_i < 4; ++dp_i) {
      sum = mod_add(sum, sumdp[vec_i][dp_i]);
    }
  } else if (curr_dp >= 2 && curr_dp <= 3) {
    for (long long vec_i = (long long)(seg_vec.size() - 1); vec_i >= 0;
         --vec_i) {
      start = seg_vec[vec_i];
      if (vec_i == (long long)(seg_vec.size()) - 1) {
        for (long long dp_i = 0; dp_i < 4; ++dp_i) {
          if (dp_i == curr_dp) {
            sumdp[vec_i][dp_i] = 0;
          } else {
            sumdp[vec_i][dp_i] = dp[start][dp_i];
          }
        }
      } else {
        for (long long dp_i = 0; dp_i < 4; ++dp_i) {
          long long pre_sum = 0;
          for (long long pre_dp_i = 0; pre_dp_i < 4; ++pre_dp_i) {
            if (checkCompatible(dp_i, pre_dp_i)) {
              pre_sum = mod_add(pre_sum, sumdp[vec_i + 1][pre_dp_i]);
            }
          }
          pre_sum = mod_mult(pre_sum, dp[start][dp_i]);
          sumdp[vec_i][dp_i] = pre_sum;
        }
      }
      pre_start = start;
    }
    sum = 0;
    long long vec_i = 0;
    for (long long dp_i = 0; dp_i < 4; ++dp_i) {
      sum = mod_add(sum, sumdp[vec_i][dp_i]);
    }
  } else {
    for (long long vec_i = 0; vec_i < (long long)(seg_vec.size()); ++vec_i) {
      start = seg_vec[vec_i];
      if (vec_i == 0) {
        for (long long dp_i = 0; dp_i < 4; ++dp_i) {
          sumdp[vec_i][dp_i] = dp[start][dp_i];
        }
      } else {
        for (long long dp_i = 0; dp_i < 4; ++dp_i) {
          long long pre_sum = 0;
          for (long long pre_dp_i = 0; pre_dp_i < 4; ++pre_dp_i) {
            if (checkCompatible(pre_dp_i, dp_i)) {
              pre_sum = mod_add(pre_sum, sumdp[vec_i - 1][pre_dp_i]);
            }
          }
          pre_sum = mod_mult(pre_sum, dp[start][dp_i]);
          sumdp[vec_i][dp_i] = pre_sum;
        }
      }
      pre_start = start;
    }
    sum = 0;
    long long vec_i = (long long)(seg_vec.size() - 1);
    for (long long dp_i = 0; dp_i < 4; ++dp_i) {
      sum = mod_add(sum, sumdp[vec_i][dp_i]);
    }
  }
  return sum;
}
void ColBracket149D::TreeDpHelper(string str, vector<long long> index_vec,
                                  long long start, long long end,
                                  long long depth) {
  if (start == end - 1) {
    for (long long dp_i = 0; dp_i < 4; ++dp_i) {
      dp[start][dp_i] = 1;
    }
    return;
  }
  vector<long long> seg_vec;
  for (long long curr_start = start, curr_end = -2; curr_end != end - 1;
       curr_start = curr_end) {
    ++curr_start;
    curr_end = index_vec[curr_start];
    TreeDpHelper(str, index_vec, curr_start, curr_end, depth + 1);
    seg_vec.push_back(curr_start);
  }
  if (depth == 0) {
    long long dpVal = getDpValue(4, seg_vec);
    dp[start][4] = dpVal;
  } else {
    for (long long dp_i = 0; dp_i < 4; ++dp_i) {
      long long dpVal = getDpValue(dp_i, seg_vec);
      dp[start][dp_i] = dpVal;
    }
  }
  return;
}
long long ColBracket149D::Dynamic(string str) {
  str = '(' + str;
  str += ')';
  vector<long long> index_vec = ParenMatch(str);
  memset(dp, 0, sizeof(dp));
  TreeDpHelper(str, index_vec, 0, (long long)(str.size()) - 1);
  long long sum = 0;
  for (long long dp_i = 0; dp_i < 5; ++dp_i) {
    sum = mod_add(sum, dp[0][dp_i]);
  }
  return sum;
}
int main() {
  ColBracket149D c;
  c.input();
  c.output();
  return 0;
}