public static int pageCount(int n, int p)
    {
        int totalFlips = n/2;
        int fromStart = 0;
        int fromEnd  = 0;
        
        /* Generalize to even page count.
           like 0, 2, 4, 6, 8......
        */
        p = p % 2 == 0 ? p : p - 1;
        
        fromStart = p/2;
        fromEnd = totalFlips - fromStart;
        
        return fromStart >= fromEnd ? fromEnd : fromStart;
            
    }

public static int pageCount(int n, int p) {
    int front = p / 2;
    int back = (n - p) / 2;
        //This handles an edge case where we want 
        //the formula above to actually be 1 (not 0)
        //when n is even and p is one less than n
    if (n - p == 1 && n % 2 == 0) back++;
    if (front < back) {
        return front;
    }   else {
        return back;
    }
}

if(n >= 1 and n <= 10**5 and p >= 1 and p <= n):
        front_flips = p // 2
        total_flips = n // 2
        back_flips = total_flips - front_flips
        if(front_flips <= back_flips):
            return front_flips
        else:
            return back_flips

public static int pageCount(int n, int p) {
    // Write your code here
        if (p == 1 || p == n || (n % 2 == 1 && p == n - 1)) {
            return 0;
        }
        
        int res = 0;
        if (n - p > n / 2) {
            // p is on first half
            res = p / 2;
        } else {
            // p is on second half
            res = (n - p) / 2;
            res = res == 0 ? 1 : res;
        }
        return res;
    }