Sophisticated Device

You are given integers $d$ and $p$, $p$ is prime.

Also you have a mysterious device. It has memory cells, each contains an integer between $0$ and $p-1$. Also two instructions are supported, addition and raising to the $d$-th power. Both are modulo $p$.

The memory cells are numbered $1,2,\cdots ,5000$. Initially cells $1$ and $2$ contain integers $x$ and $y$, respectively $(0\le x,y\le p-1)$. All other cells contain $\text{1}$s.

You cannot directly access values in cells, and you don't know values of $x$ and $y$ (but you know they are written in first two cells). You mission, should you choose to accept it, is to write a program using the available instructions to obtain the product $xy$ modulo $p$ in one of the cells. You program should work for all possible $x$ and $y$.

Addition instruction evaluates sum of values in two cells and writes it to third cell. This instruction is encoded by a string "+ e1 e2 to", which writes sum of values in cells e1 and e2 into cell to. Any values of e1, e2, to can coincide.

Second instruction writes the $d$-th power of a value in some cell to the target cell. This instruction is encoded by a string "^ e to". Values e and to can coincide, in this case value in the cell will be overwritten.

Last instruction is special, this is the return instruction, and it is encoded by a string "f target". This means you obtained values $xy$ mod $p$ in the cell target. No instructions should be called after this instruction.

Provide a program that obtains $xy$ mod $p$ and uses no more than $5000$ instructions (including the return instruction).

It is guaranteed that, under given constrains, a solution exists.

Input

The first line contains space-separated integers $d$ and $p(2\le d\le 10,d<p,3\le p\le 10^9+9,p\text{ is prime})$.

Output

Output instructions, one instruction per line in the above format. There should be no more than $5000$ lines, and the last line should be the return instruction.

Examples

This problem has no sample tests. A sample output is shown below. Note that this output is not supposed to be a solution to any testcase and is there purely to illustrate the output format.

+ 1 1 3
^ 3 3
+ 3 2 2
+ 3 2 3
^ 3 1
f 1

Here's a step-by-step runtime illustration:

Suppose that $d=2$ and $p=3$. Since for $x=0$ and $y=1$, the returned result is $1\ne 0\cdot 1$ mod $3$, this program would be judged as incorrect.