Leo has developed a new programming language C+=. In C+=, integer variables can only be changed with a "+=" operation that adds the right-hand side value to the left-hand side variable. For example, performing "a += b" when a = 2, b = 3 changes the value of a to 5 (the value of b does not change).

In a prototype program Leo has two integer variables a and b, initialized with some positive values. He can perform any number of operations "a += b" or "b += a". Leo wants to test handling large integers, so he wants to make the value of either a or b strictly greater than a given value n. What is the smallest number of operations he has to perform?

Input

The first line contains a single integer T (1 ≤ T ≤ 100) — the number of test cases.

Each of the following T lines describes a single test case, and contains three integers a, b, n (1 ≤ a, b ≤ n ≤ 10^9) — initial values of a and b, and the value one of the variables has to exceed, respectively.

Output

For each test case print a single integer — the smallest number of operations needed. Separate answers with line breaks.

Example

Input


2
1 2 3
5 4 100


Output


2
7

Note

In the first case we cannot make a variable exceed 3 in one operation. One way of achieving this in two operations is to perform "b += a" twice.
import java.util.*;
import java.lang.*;
import java.io.*;
public class ProblemA {
   public static void main (String[]args) {
   
      Scanner it = new Scanner (System.in);
      int numCase = it.nextInt();
      it.nextLine();
      String [] all = new String [numCase];
      int [] ans = new int [numCase];
      for (int y = 0; y < numCase; y++) {
       all[y] = it.nextLine();
      }
      for (int x = 0; x < numCase; x++){
         String use = all[x];
         String[] strArr = use.split("\\s+");
         int a = Integer.parseInt(strArr[0]);
         int b = Integer.parseInt(strArr[1]);
         int n = Integer.parseInt(strArr[2]);
         int count = 0;
         while (!(a > n)&& !(b > n)){
         if (getMax(a,b) == a) {
         b += a;
         count++;
         }
         else{
         a += b;
         count++;
         }
         }
         ans[x] = count;
      }
      for (int z = 0; z < numCase; z++){
      System.out.println(ans[z]);
      }
   
   }
   
   public static int getMax(int x, int y) {
   if (y > x) {
   return y;
   }
   else {
   return x;
   }
   }
}