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.Scanner;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.*;
import java.util.List;
import java.lang.Math;
import java.util.HashMap;
public class javasample {
	public static int useBs(char[] arr, char targetValue) {	
		int a =  Arrays.binarySearch(arr, targetValue);
		if(a >=0 && a<arr.length)
			return a;
		else
			return -1;
	}
	public static void printArray(int []a) {
		for(int i=0;i<a.length;i++) {
			System.out.println(a[i]+" ");
		}
		System.out.println();
	}
	public static void printArrayLong(long []a) {
		for(int i=0;i<a.length;i++) {
			System.out.println(a[i]+" ");
		}
		System.out.println();
	}
	static boolean isPalindrome(String s) {
		int l=s.length();
		for(int i=0;i<l/2;i++)
		{
			if(s.charAt(i)!=s.charAt(l-i-1))
				return false;
		}
		return true;
	}
	static String revString(String str)
	{
		return new StringBuffer(str).reverse().toString();
	}
	static String sortString(String s) {
		char a[]=s.toCharArray();
		Arrays.sort(a);
		return new String(a);
	}
	static int sumList(List<Integer>a) {
		return a.stream().mapToInt(Integer::intValue).sum();
	}
	static int sumArray(int []a) {
		int sum=0;
		for(int i=0;i<a.length;i++) {
			sum+=a[i];
		}
		return sum;
	}
    public static void main(String[]args) {
    	Scanner sc=new Scanner(System.in);
    	int t=sc.nextInt();
    	while(t-->0) {
		int a=sc.nextInt(),b=sc.nextInt(),c=sc.nextInt();
		if(b>a) {
			int temp=b;
			b=a;
			a=temp;
		}
		int cnt=0;
		while(a<=c) {
			b+=a;
			if(b>a) {
				int temp=b;
				b=a;
				a=temp;
			}
			cnt+=1;
		}
		System.out.println(cnt);
    	}
    }
}
    


