Bob has an array of length \(n\) whose elements lie in the range \([1,n]\). He compared the adjacent elements of the array and prepared a string \(s\) of length \(n -1\) of \(<\), \(>\), and  \(=\) signs that show the result of the comparison between the adjacent elements of the array. 

Formally,

• If \(s[i] : \ <\), then \(a[i] < a[i+1]\).
• If \(s[i] : \ >\), then \(a[i] > a[i+1]\).
• If \(s[i] :\ =\), then \(a[i] = a[i+1]\).
• For each valid index \(i\)

Unfortunately, Bob lost the array and now he wonders how many distinct arrays of length \(n\) exist such that its elements are between \(1\) and \(n\). Since the count can be very large, find this count modulo \(10^9 + 7\). 

Two arrays are different if they differ at least one index.

Input format 

• The first line contains a number that denotes the length of the array.
• The second line contains a string \(s\) of length \(n-1\). 

Output format 

Print the number of different arrays modulo \(10^9 + 7\).

Constraints

\(2 \le n \le 5 \times 10^3 \\ \text{s contains only <, >, and =}\)