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 min_step(num1,num2,end,temp):
    if (num1 or num2) > end :
        #print('mun1,num2,end,temp', num1, num2,end,temp)
        return temp
    else:
        x = min(num1, num2)
        y = max(num1, num2)
        x += y
        temp += 1
        #print('mun1,num2,x,y,temp',num1,num2,x,y,temp)
        return min_step(x, y, end, temp)



if __name__ == '__main__':
    trial= int(input())
    for i in range(trial):
        a,b,n= map(int, input().split())
        #print('abn' , a,b,n)
        print(min_step(a,b,n,0))