#include <stdio.h>

void multiply(int F[2][2], int M[2][2]);

void power(int F[2][2], int n);

/* function that returns nth Fibonacci number */
int fib(int n)
{
int F[2][2] = {{1,1},{1,0}};
if (n == 0)
    return 0;
power(F, n-1);
return F[0][0];
}

/* Optimized version of power() in method 4 */
void power(int F[2][2], int n)
{
if( n == 0 || n == 1)
    return;
int M[2][2] = {{1,1},{1,0}};

power(F, n/2);
multiply(F, F);

if (n%2 != 0)
    multiply(F, M);
}

void multiply(int F[2][2], int M[2][2])
{
int x = F[0][0]*M[0][0] + F[0][1]*M[1][0];
int y = F[0][0]*M[0][1] + F[0][1]*M[1][1];
int z = F[1][0]*M[0][0] + F[1][1]*M[1][0];
int w = F[1][0]*M[0][1] + F[1][1]*M[1][1];

F[0][0] = x;
F[0][1] = y;
F[1][0] = z;
F[1][1] = w;
}

/* Driver program to test above function */
int main()
{
int n = 9;
printf("%d", fib(9));
getchar();
return 0;
}