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.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
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);
        _1007B solver = new _1007B();
        solver.solve(1, in, out);
        out.close();
    }

    static class _1007B {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            List[] fl = new List[100001];

            for (int i = 1; i <= 100000; i++) {
                fl[i] = factors(i);
            }

            int t = in.nextInt();

            NextPermutation np = new NextPermutation();


            while (t-- > 0) {
                int[] a = new int[3];

                a[0] = in.nextInt();
                a[1] = in.nextInt();
                a[2] = in.nextInt();

                Arrays.sort(a);

                long fans = 0;

                do {
                    int f = 0;
                    int s = 0;

                    int num = a[1];

                    long ans = 0;
                    for (int i = 0; i < fl[num].size(); i++) {
                        int cnum = (int) fl[num].get(i);
                        while (f < fl[a[0]].size() && (int) fl[a[0]].get(f) <= cnum) {
                            f++;
                        }
                        f--;

                        while (s < fl[a[2]].size() && (int) fl[a[2]].get(s) < cnum) {
                            s++;
                        }

                        ans += (((long) f + 1) * (fl[a[2]].size() - s));
                    }

                    fans = Math.max(fans, ans);
                } while ((a = np.nextPermutation(a)) != null);

                out.println(fans);
            }
        }

        List<Integer> factors(int n) {
            List<Integer> factors = new ArrayList<>();

            for (int i = 1; i * i <= n; i++) {
                if (n % i == 0) {
                    factors.add(i);
                    if (i != n / i)
                        factors.add(n / i);
                }
            }

            factors.sort((x, y) -> x - y);

            return factors;
        }

        class NextPermutation {
            public int[] nextPermutation(int[] nums) {
                if (nums == null || nums.length < 2)
                    return null;

                int p = 0;
                for (int i = nums.length - 2; i >= 0; i--) {
                    if (nums[i] < nums[i + 1]) {
                        p = i;
                        break;
                    }
                }

                int q = 0;
                for (int i = nums.length - 1; i > p; i--) {
                    if (nums[i] > nums[p]) {
                        q = i;
                        break;
                    }
                }

                if (p == 0 && q == 0) {
                    reverse(nums, 0, nums.length - 1);
                    return null;
                }

                int temp = nums[p];
                nums[p] = nums[q];
                nums[q] = temp;

                if (p < nums.length - 1) {
                    reverse(nums, p + 1, nums.length - 1);
                }

                return nums;
            }

            public void reverse(int[] nums, int left, int right) {
                while (left < right) {
                    int temp = nums[left];
                    nums[left] = nums[right];
                    nums[right] = temp;
                    left++;
                    right--;
                }
            }

        }

    }

    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 println(long i) {
            writer.println(i);
        }

    }

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

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

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

        }

    }
}

