You are given a rectangular parallelepiped with sides of positive integer lengths A, B and C. 

Find the number of different groups of three integers (a, b, c) such that 1≤ a≤ b≤ c and parallelepiped A× B× C can be paved with parallelepipeds a× b× c. Note, that all small parallelepipeds have to be rotated in the same direction.

For example, parallelepiped 1× 5× 6 can be divided into parallelepipeds 1× 3× 5, but can not be divided into parallelepipeds 1× 2× 3.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each of the next t lines contains three integers A, B and C (1 ≤ A, B, C ≤ 10^5) — the sizes of the parallelepiped.

Output

For each test case, print the number of different groups of three points that satisfy all given conditions.

Example

Input

4
1 1 1
1 6 1
2 2 2
100 100 100


Output

1
4
4
165

Note

In the first test case, rectangular parallelepiped (1, 1, 1) can be only divided into rectangular parallelepiped with sizes (1, 1, 1).

In the second test case, rectangular parallelepiped (1, 6, 1) can be divided into rectangular parallelepipeds with sizes (1, 1, 1), (1, 1, 2), (1, 1, 3) and (1, 1, 6).

In the third test case, rectangular parallelepiped (2, 2, 2) can be divided into rectangular parallelepipeds with sizes (1, 1, 1), (1, 1, 2), (1, 2, 2) and (2, 2, 2). 
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskB solver = new TaskB();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++) {
            solver.solve(i, in, out);
        }
        out.close();
    }

    static class TaskB {
        long[] numDivisors = MultiplicativeFunction.DIVISOR_COUNT.calculateUpTo(100001);

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int a = in.readInt();
            int b = in.readInt();
            int c = in.readInt();
            long answer = 0;
            int ab = IntegerUtils.gcd(a, b);
            int bc = IntegerUtils.gcd(b, c);
            int ac = IntegerUtils.gcd(a, c);
            int abc = IntegerUtils.gcd(ab, c);
            long exactA = numDivisors[a] - numDivisors[ab] - numDivisors[ac] + numDivisors[abc];
            answer += exactA *
                    (numDivisors[b] * numDivisors[c] - numDivisors[bc] * (numDivisors[bc] - 1) / 2);
            long exactB = numDivisors[b] - numDivisors[ab] - numDivisors[bc] + numDivisors[abc];
            answer += exactB *
                    (numDivisors[a] * numDivisors[c] - numDivisors[ac] * (numDivisors[ac] - 1) / 2);
            long exactC = numDivisors[c] - numDivisors[ac] - numDivisors[bc] + numDivisors[abc];
            answer += exactC *
                    (numDivisors[b] * numDivisors[a] - numDivisors[ab] * (numDivisors[ab] - 1) / 2);
            answer -= exactA * exactB * numDivisors[c];
            answer -= exactB * exactC * numDivisors[a];
            answer -= exactA * exactC * numDivisors[b];
            answer += exactA * exactB * exactC;
            long exactAB = numDivisors[ab] - numDivisors[abc];
            long exactBC = numDivisors[bc] - numDivisors[abc];
            long exactAC = numDivisors[ac] - numDivisors[abc];
            answer += exactAB * exactBC * exactAC;
            answer += exactAB * (exactAB + 1) / 2 * (exactAC + exactBC);
            answer += exactBC * (exactBC + 1) / 2 * (exactAB + exactAC);
            answer += exactAC * (exactAC + 1) / 2 * (exactAB + exactBC);
            answer += numDivisors[abc] * exactBC * (exactBC + 1) / 2;
            answer += numDivisors[abc] * exactAB * (exactAB + 1) / 2;
            answer += numDivisors[abc] * exactAC * (exactAC + 1) / 2;
            answer += numDivisors[abc] * (exactAB * exactAC + exactAB * exactBC + exactAC * exactBC);
            answer += numDivisors[abc] * (numDivisors[abc] + 1) / 2 * (exactAB + exactAC + exactBC);
            answer += numDivisors[abc] * (numDivisors[abc] + 1) * (numDivisors[abc] + 2) / 6;
            out.printLine(answer);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        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 int readInt() {
            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 String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static abstract class MultiplicativeFunction {
        public static final MultiplicativeFunction DIVISOR_COUNT = new MultiplicativeFunction() {

            protected long value(long p, int exponent, long power) {
                return exponent + 1;
            }
        };

        protected abstract long value(long p, int exponent, long power);

        public long[] calculateUpTo(int upTo) {
            int[] divisor = IntegerUtils.generateDivisorTable(upTo);
            long[] result = new long[upTo];
            if (upTo <= 1) {
                return result;
            }
            result[1] = 1;
            for (int i = 2; i < upTo; i++) {
                int iDivided = i;
                int exponent = 0;
                do {
                    iDivided /= divisor[i];
                    exponent++;
                } while (iDivided % divisor[i] == 0);
                result[i] = result[iDivided] * value(divisor[i], exponent, i / iDivided);
            }
            return result;
        }

    }

    static class IntegerUtils {
        public static int gcd(int a, int b) {
            a = Math.abs(a);
            b = Math.abs(b);
            while (b != 0) {
                int temp = a % b;
                a = b;
                b = temp;
            }
            return a;
        }

        public static int[] generateDivisorTable(int upTo) {
            int[] divisor = new int[upTo];
            for (int i = 1; i < upTo; i++) {
                divisor[i] = i;
            }
            for (int i = 2; i * i < upTo; i++) {
                if (divisor[i] == i) {
                    for (int j = i * i; j < upTo; j += i) {
                        divisor[j] = i;
                    }
                }
            }
            return divisor;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }
}

