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
input = sys.stdin.readline

############ Input Functions ################

# Take integer input
def inp():
    return(int(input()))
# Take list input
def inlt():
    return(list(map(int, input().split())))
# Take string as list of characters
def insr():
    s = input()
    return(s[:len(s) - 1])
# Take space separated integer variable inputs
def invr():
    return(map(int, input().split()))

################ Solution ##################
def solve(t):
    a, b, n = t
    
    steps = 0
    while a <= n and b <= n:
        if a >= b:
            b += a
        else:
            a += b        
        steps += 1
    print(steps)

################ Read Input ################
T = inp()
tests = []
for _ in range(T):
    # tests.append(inp())
    # tests.append(insr())

    # inp()
    tests.append(inlt())
    # tests.append(invr())

for t in tests:
    solve(t)
