Problem: Little X used to play a card game called "24 Game", but recently he has found it too easy. So he invented a new game.

Initially you have a sequence of n integers: 1, 2, ..., n. In a single step, you can pick two of them, let's denote them a and b, erase them from the sequence, and append to the sequence either a + b, or a - b, or a × b.

After n - 1 steps there is only one number left. Can you make this number equal to 24?

Input

The first line contains a single integer n (1 ≤ n ≤ 105).

Output

If it's possible, print "YES" in the first line. Otherwise, print "NO" (without the quotes).

If there is a way to obtain 24 as the result number, in the following n - 1 lines print the required operations an operation per line. Each operation should be in form: "a op b = c". Where a and b are the numbers you've picked at this operation; op is either "+", or "-", or "*"; c is the result of corresponding operation. Note, that the absolute value of c mustn't be greater than 1018. The result of the last operation must be equal to 24. Separate operator sign and equality sign from numbers with spaces.

If there are multiple valid answers, you may print any of them.

Examples

Input

1


Output

NO


Input

8


Output

YES
8 * 7 = 56
6 * 5 = 30
3 - 4 = -1
1 - 2 = -1
30 - -1 = 31
56 - 31 = 25
25 + -1 = 24

Solution (in JAVA):

Solution:
import java.util.Scanner;

/**
 * @Description 24点游戏
 * @Author wangli
 * @Email li.wang9808@gmail.com
 * @Date 2020/8/16
 * @Version 1.2
 */
public class Algorithm01 {
    /**
     * 物品数量n
     */
    private static Integer n;

    public static void main(String[] args) {
        //System.out.println("Please enter a number: ");
        Scanner scanner = new Scanner(System.in);
        while (scanner.hasNext()) {
            if (scanner.hasNextInt()) {
                n = scanner.nextInt();
                if (n >= 4 && n % 2 == 0) {
                    printNumbersExceptFourOrFive(4);
                    printFour();
                } else if (n >= 5 && n % 2 != 0) {
                    printNumbersExceptFourOrFive(5);
                    printFive();
                } else {
                    System.out.println("NO");
                }
            } else {
                System.out.println("Please enter the correct data type");
                break;
            }
        }
    }

    /**
     * 打印1-4或者1-5之外的数字进行的运算
     *
     * @param number 4 or 5
     */
    public static void printNumbersExceptFourOrFive(int number) {
        System.out.println("YES");
        for (int i = number + 1; i <= n - 1; i += 2) {
            int num1 = i + 1;
            int num2 = i + 3;
            System.out.println(num1 + " - " + i + " = " + 1);
            if (num2 <= n) {
                System.out.println(1 + " * " + num2 + " = " + num2);
            }
        }
        if (n != 4 && n != 5) {
            System.out.println("1 * 1 = 1");
        }
    }

    /**
     * 打印1-4得出结果为24的运算过程
     */
    public static void printFour() {
        System.out.println("1 + 2 = 3");
        System.out.println("3 + 3 = 6");
        System.out.println("6 * 4 = 24");
    }

    /**
     * 打印1-5得出结果为24的运算过程
     */
    public static void printFive() {
        System.out.println("1 + 5 = 6");
        System.out.println("6 - 3 = 3");
        System.out.println("3 * 2 = 6");
        System.out.println("6 * 4 = 24");
    }
}