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.
#Techcoder
import sys
import os.path
import math
import copy
from sys import stdin,stdout
from collections import*
from math import gcd,ceil,floor
mod = int(1e9+7)
m1=float("inf")
##sys.setrecursionlimit(10**8)
#input=sys.stdin.readline

if os.path.exists('Updated prg/Input3d.txt'):
    sys.stdout=open("Updated prg/Output3d.txt","w")
    sys.stdin=open("Updated prg/Input3d.txt","r")
 
def sinp():return input()
def ninp():return int(sinp())
def mapinp():return map(int,sinp().split())
def smapinp():return map(str,sinp().split())
def linp():return list(mapinp())
def sl():return list(sinp().split())
def power(n):return 1<<n
def prnt(a):print(a)
def prntl(a):print(a,end=" ")
def prntlist(l1):print(*l1)

for _ in range(ninp()):
    a,b,n=mapinp()
    c=0
    while a<=n and b<=n:
        maxi=max(a,b)
        if maxi!=a:
            a=a+b
            c=c+1
        else:
            b=b+a
            c=c+1
    prnt(c)