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 math

def primeFactors(n): 
    dic = set([n])
    
    while n % 2 == 0: 
        dic.add(2)
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            dic.add(i)
            n = n / i 
    if n > 2: 
        dic.add(n)

    return sorted(list(dic))

def twoStacks(x, a, b):
    a = [0]+a
    indexA = 0
    for i in range(1,len(a)):
        a[i]+=a[i-1]
        if a[i]<=x: indexA = i
        else: break

    for i in range(1,len(b)):
        b[i]+=b[i-1]

    indexB = 0
    ans = 0
    for i in range(indexA,-1,-1):
        sum = a[i]
        t = i
        secIndex = -1
        j = 0
        for j in range(indexB,len(b)):
            if sum+b[j]<=x: secIndex = j
            else:break
        
        t += secIndex+1
        indexB = j
        if t > ans: ans = t
    return ans

for _ in range(int(input())):
    a,b,n = map(int,input().split())

    maxV = max(a,b)
    minV = min(a,b)
    ans = 0
    while(maxV<=n):
        minV += maxV
        if minV>maxV: maxV,minV = minV,maxV
        ans+=1
    print(ans)
    