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 sys
# sys.stdin = open('input.txt', 'r') 
# sys.stdout = open('output.txt', 'w')
 
import math
import collections
from sys import stdin,stdout,setrecursionlimit
import bisect as bs
setrecursionlimit(2**20)
M = 10**9+7
 
T = int(stdin.readline())
# T = 1      
a = [0,1]
for i in range(50):
    a.append(a[-1]+a[-2])
b = [1,1]
for i in range(50):
    b.append(b[-1]+b[-2])

for _ in range(T):
    # n = int(stdin.readline())
    x,y,n = list(map(int,stdin.readline().split()))
    # a = list(map(int,stdin.readline().split()))
    # b = list(map(int,stdin.readline().split()))
    # q = list(map(int,stdin.readline().split()))
    # b = list(map(int,stdin.readline().split()))
    # s = stdin.readline().strip('\n')
    A = min(x,y)
    B = max(x,y)
    for i in range(52):
        if(A*a[i] + B*b[i] > n):
            print(i)
            break
