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.util.*;
import java.io.*;
import java.awt.*;
public class Main{
    public static void main(String[] args){
        InputReader sc = new InputReader(System.in);
        StringBuilder sb = new StringBuilder();
        int t = sc.nextInt();
        while(t --> 0){
            int a = sc.nextInt(),b = sc.nextInt(),n = sc.nextInt();
            int count = 0;
            while(a+b <= n){
                if(a>b)b+=a;
                else a+=b;
                count++;
            }
            count++;
            System.out.println(count);
        }
        
    }
}
class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
    public int read() {
        if (numChars==-1) throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try { numChars = stream.read(buf); }
            catch (IOException e) { throw new InputMismatchException(); }

            if(numChars <= 0) return -1;
        }
        return buf[curChar++];
    }
    public String nextLine() {
        String str = "";
        try { str = br.readLine(); }
        catch (IOException e) { e.printStackTrace(); }
        return str;
    }
    public int nextInt() {
        int c = read();
        while(isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if(c<'0'||c>'9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }
    public long nextLong() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }
    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9') throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
    public String readString() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        }
        while (!isSpaceChar(c));
        return res.toString();
    }
    public boolean isSpaceChar(int c) {
        if (filter != null) return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    public String next() { return readString();}
    public interface SpaceCharFilter { public boolean isSpaceChar(int ch);}
}