Alice and Bob are playing an array game. Initially, each of them has an array of length ~N~. Alice's array is ~A = [a_1, a_2, \dots, a_N]~ and Bob's array is ~B = [b_1, b_2, \dots, b_N]~, where all ~a_i~ and ~b_i~ are positive integers.

Alice may perform any number of operations (including zero). In a single operation, she chooses a contiguous interval ~[L, R]~ (~1 \le L < R \le N~) and replaces every element in that interval by the maximum value over that interval. Formally, she computes ~M = \max_{\,L \le j \le R} a_j~, and then for every ~i~ (~L \le i \le R~) sets ~a_i = M~.

After Alice finishes all her operations, she compares her final array ~A~ to Bob's array ~B~. She scores one point for each index ~i~ where ~a_i = b_i~. Compute the maximum number of points Alice can get by choosing her operations optimally.

Input Specification

The first line contains an integer ~N~ (~1 \le N \le 10^5~), the length of the arrays.

The second line contains ~N~ integers ~a_i~, (~1 \le a_i \le 10^9~), indicating Alice's array.

The third line contains ~N~ integers ~b_i~, (~1 \le b_i \le 10^9~), indicating Bob's array.

Output Specification

Print a single integer, the maximum number of points Alice can achieve.

Constraints

Subtask	Points	Additional constraints
~1~	~14~	~N \le 10~
~2~	~16~	~N \le 200~.
~3~	~13~	~N \le 5\,000~ and the array ~A~ is strictly increasing ~(a_1 < a_2 < \dots < a_N)~.
~4~	~22~	~N \le 5\,000~.
~5~	~12~	All ~b_i~ are the same (~b_1 = b_2 = \cdots = b_N~).
~6~	~23~	No additional constraints

Sample Input

4
10 2 9 2
10 9 10 9

Sample Output

3

Explanation for Sample

Alice can choose the interval ~[2, 4]~ and change the array to ~[10, 9, 9, 9]~, then she can get ~3~ points. There is no way to get more points.