Given the **length N** of the string, we have to find the number of special strings of length N.

A string is called a special string if it consists only of **lowercase letters a and b** and **there is at least one b between two a’s in the string**. Since the number of strings may be very large, therefore print it modulo 10^9+7.

**Examples:**

Input:N = 2

Output:3

Explanation :

The number of special string so length 2 are 3 i.e. “ab”, “ba”, “bb”

Input:N = 3

Output:5

Explanation:

The number of special string so length 3 are 5 i.e. “abb”, “aba”, “bab”, “bba”, “bbb”

**Approach:**

To solve the problem mentioned above, the first observation is if the integer N is 0 then there can only be an empty string as the answer, if N is 1 then there can be two string “a” or “b” as an answer but if the value of N is greater than 1 then the answer is equal to the sum of previous two terms. Now to find the count of special strings we run a loop and for each integer i count of the special string of length i is equal to the sum of the count of special strings of length i-1 and count of special strings of length i-2. Store the value of each integer in an array and return the required answer.

Below is the implementation of the above approach:

## C++

`// C++ Program to Count the number ` `// of Special Strings of a given length N ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` `#define mod 1000000007 ` ` ` `// Function to return count of special strings ` `long` `count_special(` `long` `n) ` `{ ` ` ` `// stores the answer for a ` ` ` `// particular value of n ` ` ` `long` `fib[n + 1]; ` ` ` ` ` `// for n = 0 we have empty string ` ` ` `fib[0] = 1; ` ` ` ` ` `// for n = 1 we have ` ` ` `// 2 special strings ` ` ` `fib[1] = 2; ` ` ` ` ` `for` `(` `int` `i = 2; i <= n; i++) { ` ` ` ` ` `// calculate count of special string of length i ` ` ` `fib[i] = (fib[i - 1] % mod + fib[i - 2] % mod) % mod; ` ` ` `} ` ` ` ` ` `// fib[n] stores the count ` ` ` `// of special strings of length n ` ` ` `return` `fib[n]; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` ` ` `// initialise n ` ` ` `long` `n = 3; ` ` ` ` ` `cout << count_special(n) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count the number of ` `// special strings of a given length N ` `import` `java.util.*; ` ` ` `class` `GFG{ ` ` ` `static` `final` `int` `mod = ` `1000000007` `; ` ` ` `// Function to return count of ` `// special Strings ` `static` `int` `count_special(` `int` `n) ` `{ ` ` ` ` ` `// Stores the answer for a ` ` ` `// particular value of n ` ` ` `int` `[]fib = ` `new` `int` `[n + ` `1` `]; ` ` ` ` ` `// For n = 0 we have empty String ` ` ` `fib[` `0` `] = ` `1` `; ` ` ` ` ` `// For n = 1 we have ` ` ` `// 2 special Strings ` ` ` `fib[` `1` `] = ` `2` `; ` ` ` ` ` `for` `(` `int` `i = ` `2` `; i <= n; i++) ` ` ` `{ ` ` ` ` ` `// Calculate count of special ` ` ` `// String of length i ` ` ` `fib[i] = (fib[i - ` `1` `] % mod + ` ` ` `fib[i - ` `2` `] % mod) % mod; ` ` ` `} ` ` ` ` ` `// fib[n] stores the count of ` ` ` `// special Strings of length n ` ` ` `return` `fib[n]; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` ` ` `// Initialise n ` ` ` `int` `n = ` `3` `; ` ` ` ` ` `System.out.print(count_special(n) + ` `"\n"` `); ` `} ` `} ` ` ` `// This code is contributed by sapnasingh4991 ` |

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## Python3

`# Python3 program to count the number ` `# of special strings of a given length N ` `mod ` `=` `1000000007` ` ` `# Function to return count of ` `# special strings ` `def` `count_special(n): ` ` ` ` ` `# Stores the answer for a ` ` ` `# particular value of n ` ` ` `fib ` `=` `[` `0` `for` `i ` `in` `range` `(n ` `+` `1` `)] ` ` ` ` ` `# For n = 0 we have empty string ` ` ` `fib[` `0` `] ` `=` `1` ` ` ` ` `# For n = 1 we have ` ` ` `# 2 special strings ` ` ` `fib[` `1` `] ` `=` `2` ` ` ` ` `for` `i ` `in` `range` `(` `2` `, n ` `+` `1` `, ` `1` `): ` ` ` ` ` `# Calculate count of special ` ` ` `# string of length i ` ` ` `fib[i] ` `=` `(fib[i ` `-` `1` `] ` `%` `mod ` `+` ` ` `fib[i ` `-` `2` `] ` `%` `mod) ` `%` `mod ` ` ` ` ` `# fib[n] stores the count ` ` ` `# of special strings of length n ` ` ` `return` `fib[n] ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` ` ` `# Initialise n ` ` ` `n ` `=` `3` ` ` ` ` `print` `(count_special(n)) ` ` ` `# This code is contributed by Bhupendra_Singh ` |

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## C#

`// C# program to count the number of ` `// special strings of a given length N ` `using` `System; ` `class` `GFG{ ` ` ` `const` `int` `mod = 1000000007; ` ` ` `// Function to return count of ` `// special Strings ` `static` `int` `count_special(` `int` `n) ` `{ ` ` ` ` ` `// Stores the answer for a ` ` ` `// particular value of n ` ` ` `int` `[]fib = ` `new` `int` `[n + 1]; ` ` ` ` ` `// For n = 0 we have empty String ` ` ` `fib[0] = 1; ` ` ` ` ` `// For n = 1 we have ` ` ` `// 2 special Strings ` ` ` `fib[1] = 2; ` ` ` ` ` `for` `(` `int` `i = 2; i <= n; i++) ` ` ` `{ ` ` ` ` ` `// Calculate count of special ` ` ` `// String of length i ` ` ` `fib[i] = (fib[i - 1] % mod + ` ` ` `fib[i - 2] % mod) % mod; ` ` ` `} ` ` ` ` ` `// fib[n] stores the count of ` ` ` `// special Strings of length n ` ` ` `return` `fib[n]; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` ` ` `// Initialise n ` ` ` `int` `n = 3; ` ` ` ` ` `Console.Write(count_special(n) + ` `"\n"` `); ` `} ` `} ` ` ` `// This code is contributed by Nidhi_biet ` |

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**Output:**

5

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