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.


def steps(a,b,n):
    i=0
    j=0
    while i<=n:
        if a>=b:
            b+=a
            i=b
            j+=1
        else:
            a+=b
            i=a
            j+=1
    return j
    # i=0
    # j=0
    # if a>=b:
    #    b+=a
    #    b+=a
    #    j+=2
    #    i=b
    # #    print(i)
    # else:
    #    a+=b
    #    a+=b
    #    j+=2
    #    i=a
    # #    print(i)
    # if i>n:
    # #    print(i)
    #    return j
    # else:
    #     while i < n:
    #         if i==a:
    #              for i in range(2):
    #                 b+=a
    #                 j+=1
    #                 i=b
    #         elif i==b:
    #              for i in range(2):
    #                 a+=b
    #                 j+=1
    #                 i=a
    #     return j-1
   
    
    

for _ in range(int(input())):
   a,b,n = [int(x) for x in input().split()]
   ans= steps(a,b,n)
   print(ans)
    
    
