There are $N$ competitive programmers numbered person $1$, person $2$, $\ldots$, and person $N$.  
There is a relation called superiority between the programmers. For all pairs of distinct programmers $($person $X$, person $Y$$)$, exactly one of the following two relations holds: "person $X$ is stronger than person $Y$" or "person $Y$ is stronger than person $X$."  
The superiority is transitive. In other words, for all triplets of distinct programmers $($person $X$, person $Y$, person $Z$$)$, it holds that:

-   if person $X$ is stronger than person $Y$ and person $Y$ is stronger than person $Z$, then person $X$ is stronger than person $Z$.

A person $X$ is said to be the strongest programmer if person $X$ is stronger than person $Y$ for all people $Y$ other than person $X$. (Under the constraints above, we can prove that there is always exactly one such person.)

You have $M$ pieces of information on their superiority. The $i$-th of them is that "person $A_i$ is stronger than person $B_i$."  
Can you determine the strongest programmer among the $N$ based on the information?  
If you can, print the person's number. Otherwise, that is, if there are multiple possible strongest programmers, print `-1`.

The input is given from Standard Input in the following format:

```
$N$ $M$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_M$ $B_M$
```

If you can uniquely determine the strongest programmer, print the person's number; otherwise, print `-1`.

-   $2 \leq N \leq 50$
-   $0 \leq M \leq \frac{N(N-1)}{2}$
-   $1 \leq A_i, B_i \leq N$
-   $A_i \neq B_i$
-   If $i \neq j$, then $(A_i, B_i) \neq (A_j, B_j)$.
-   There is at least one way to determine superiorities for all pairs of distinct programmers, that is consistent with the given information.

1

You have two pieces of information: "person 1 is stronger than person 2" and "person 2 is stronger than person 3."
By the transitivity, you can also infer that "person 1 is stronger than person 3," so person 1 is the strongest programmer.

-1

Both person 1 and person 2 may be the strongest programmer. Since you cannot uniquely determine which is the strongest, you should print -1.