13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6a2,

After learning about polynomial hashing, Heidi decided to learn about shift-xor hashing. In particular, she came across this interesting problem.

Given a bitstring $$$y \in \{0,1\}^n$$$ find out the number of different $$$k$$$ ($$$0 \leq k \lt n$$$) such that there exists $$$x \in \{0,1\}^n$$$ for which $$$y = x \oplus \mbox{shift}^k(x).$$$

In the above, $$$\oplus$$$ is the xor operation and $$$\mbox{shift}^k$$$ is the operation of shifting a bitstring cyclically to the right $$$k$$$ times. For example, $$$001 \oplus 111 = 110$$$ and $$$\mbox{shift}^3(00010010111000) = 00000010010111$$$.

Input

The first line contains an integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$), the length of the bitstring $$$y$$$.

The second line contains the bitstring $$$y$$$.

Output

Output a single integer: the number of suitable values of $$$k$$$.

Heidi Learns Hashing (Medium)

Examples