Problem: This is an output-only problem. You shouldn't read anything from the input.

In short, your task is to simulate multiplication by using only comparison (x < y) and addition (x + y). There is no input in this problem, you just print a sequence of operations.

Imagine that there is a big array a[0], a[1], ..., a[N-1] of length N. The first two values are initially two non-negative integers A and B (which are unknown to you), the other elements are zeros. Your goal is to get the product A \cdot B in a[2] at the end.

You are allowed operations of two types, with the following format (where 0 \leq i, j, k < N):

* `+ i j k` — applies operation a[k] = a[i] + a[j].
* `< i j k` — applies operation a[k] = a[i] < a[j]. That is, if a[i] < a[j] then a[k] becomes 1, otherwise it becomes 0.



You can use at most Q operations. Elements of a can't exceed V. Indices (i, j, k) don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs (A, B) within a single test. Each time, the checker chooses values A and B, creates the array a = [A, B, 0, 0, \ldots, 0], applies all your operations and ensures that a[2] = A \cdot B.

Constraints

* 0 \leq A, B \leq 10^9
* N = Q = 200\,000
* V = 10^{19} = 10\,000\,000\,000\,000\,000\,000

Input

The Standard Input is empty.

Output

In the first line, print the number of operations. Each operation should then be printed in a single line of format `+ i j k` or `< i j k`.

Example

Input




Output

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;


public class Main {
    static int cnt = 0;
    static ArrayList<String> op = new ArrayList<>();
    static final int A = 0;
    static final int B = 1;
    static final int C = 2;
    static final int Zero = 3;
    static final int One = 4;
    static final int X = 5;
    static final int Y = 6;
    static final int Reg = 7;
    static int ptr = 8;
    static final int[] Pows = malloc(ptr, ptr += 32);
    static final int[] A_Bits = malloc(ptr, ptr += 32);
    static final int[] B_Bits = malloc(ptr, ptr += 32);
    static final int[] C_Bits = malloc(ptr, ptr += 64);

    public static void main(String[] args) throws Exception {
        // Ignore the special case: A = B = 0, because (0 < 0) = 0 and (0 + 0) = 0.

        PrepareZeroAndOne: {
            ad(A, B, Reg);                      // tmp <= A + B
            lt(Zero, Reg, One);                 // 1   <= (0 < A + B)
        }

        PreparePowerOfTwo: { // calculates 2^i (i=0,...,31) and store to Pows[i].
            for (int i = 0; i < 32; i++) {
                setOne(Pows[i]);                // Pows[i] <= 1
                shiftLeft(Pows[i], i);          // Pows[i] <= Pows[i] << i
            }
        }

        AtoBits: { // x = 0 => 2^(a_0) => 2^(a_0) + 2^(a_1) => ... => A (a_0 > a_1 > ...).
            for (int i = 31; i >= 0; i--) {
                ad(X, Pows[i], Reg);            // tmp  <= x + 2^i
                lt(A, Reg, Reg);                // tmp  <= A < tmp  (i.e. A <  x + 2^i)
                lt(Reg, One, Reg);              // tmp  <= !tmp     (i.e. A >= x + 2^i)
                ad(A_Bits[i], Reg, A_Bits[i]);  // a[i] <= tmp
                shiftLeft(Reg, i);              // tmp  <= tmp << i (i.e. if A >= x + 2^i then 2^i else 0)
                ad(X, Reg, X);                  // x    <= x + tmp
            }
        }

        BtoBits: { // y = 0 => 2^(b_0) => 2^(b_0) + 2^(b_1) => ... => B (b_0 > b_1 > ...).
            for (int i = 31; i >= 0; i--) {
                ad(Y, Pows[i], Reg);            // tmp  <= y + 2^i
                lt(B, Reg, Reg);                // tmp  <= B < tmp  (i.e. B <  y + 2^i)
                lt(Reg, One, Reg);              // tmp  <= !tmp     (i.e. B >= y + 2^i)
                ad(B_Bits[i], Reg, B_Bits[i]);  // b[i] <= tmp
                shiftLeft(Reg, i);              // tmp  <= tmp << i (i.e. if B >= y + 2^i then 2^i else 0)
                ad(Y, Reg, Y);                  // y    <= y + tmp
            }
        }
        

        Multiply: {
            /**
             *     0111 = A[3:0]
             * ×   0111 = B[3:0]
             * --------
             *     0111 = (A[0] * [B[3], B[2], B[1], B[0]]) << 0
             *    0111  = (A[1] * [B[3], B[2], B[1], B[0]]) << 1
             *   0111   = (A[2] * [B[3], B[2], B[1], B[0]]) << 2
             *  0000    = (A[3] * [B[3], B[2], B[1], B[0]]) << 3
             * --------
             * 00012321 = C[7:0] (C[k] = Σ[i+j=k] A[i] * B[j])
             * 
             * 0111 * 0111 = 0*(2^7) + 0*(2^6) + 0*(2^5) + 1*(2^4) + 2*(2^3) + 3*(2^2) + 2*(2^1) + 1*(2^0)
             * 
             * Generally, A * B = Σ[k=0,63] (Σ[i+j=k] A[i] * B[j]) << k.
             */
            for (int i = 0; i < 32; i++) {
                for (int j = 0; j < 32; j++) {
                    and(A_Bits[i], B_Bits[j], Reg);        // tmp    <= A[i] * B[j]
                    ad(C_Bits[i + j], Reg, C_Bits[i + j]); // C[i+j] <= C[i+j] + tmp
                }
            }
            for (int i = 0; i < 64; i++) {
                shiftLeft(C_Bits[i], i);        // C[i+j] <= C[i+j] << (i+j)
                ad(C, C_Bits[i], C);            // C      <= C + C[i+j]
            }
        }

        System.out.println(cnt);
        op.forEach(System.out::println);
    }

    static int[] malloc(int from, int to) {
        int[] mem = new int[to - from];
        Arrays.setAll(mem, i -> from + i);
        return mem;
    }

    static void lt(int i, int j, int dst) {
        cnt++;
        op.add(String.format("< %d %d %d", i, j, dst));
    }

    static void ad(int i, int j, int dst) {
        cnt++;
        op.add(String.format("+ %d %d %d", i, j, dst));
    }

    static void setOne(int i) {
        lt(Zero, One, i);
    }

    static void clear(int i) {
        lt(i, i, i);
    }

    static void shiftLeft(int i, int shamt) {
        for (int k = 0; k < shamt; k++) {
            ad(i, i, i);
        }
    }

    static void and(int i, int j, int dst) {
        ad(i, j, dst);
        lt(One, dst, dst);
    }
}