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 java.io.*;
import java.util.StringTokenizer;


public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        var in = new IReader();
        var out = new PrintWriter(System.out);
        var solver = new TaskA();
        solver.solve(in, out);
        out.close();
    }

    static class TaskA {
        public void solve(IReader in, PrintWriter out) {
            int len = in.nextInt();

            while(len-- > 0){
                var arr = in.readIntArr(3);

                int count = 0;
                while(arr[0] <= arr[2] && arr[1] <= arr[2]){
                    if(arr[0] < arr[1]){
                        arr[0]+=arr[1];
                    } else{
                        arr[1] += arr[0];
                    }
                    count++;
                }
                out.println(count);
            }
        }
    }

    static class IReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public IReader(){
            this.reader = new BufferedReader(new InputStreamReader(System.in));
            this.tokenizer = new StringTokenizer("");
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int[] readIntArr(final int len){
            int[] arr = new int[len];
            for(int i=0; i < len; ++i){
                arr[i] = nextInt();
            }
            return arr;
        }
        public long[] readLongArr(final int len){
            long[] arr = new long[len];
            for(int i=0; i < len; ++i){
                arr[i] = nextLong();
            }
            return arr;
        }
        public String[] readStrArr(final int len){
            String[] arr = new String[len];
            for(int i=0; i < len; ++i){
                arr[i] = next();
            }
            return arr;
        }
        public double[] readDoubleArr(final int len){
            double[] arr = new double[len];
            for(int i=0; i < len; ++i){
                arr[i] = nextDouble();
            }
            return arr;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}