#include <bits/stdc++.h>
using namespace std;

const int DIM = 1e5 + 5;

string str;
bool ans[DIM];

int main( void ) {
    
    int n;
    cin >> n >> str;
    
    for( char &ch : str )
        ch = ( ch == 'x' );
    
    bool ok = false;
    for( int v0 = 0; v0 <= 1 && ok == false; v0 ++ ) {
    for( int v1 = 0; v1 <= 1 && ok == false; v1 ++ ) {
        ans[0] = v0; ans[1] = v1;
        
        for( int i = 2; i < n; i ++ )
            ans[i] = ( ans[i - 2] ^ ans[i - 1] ^ str[i - 1] );
        
        if( ( ans[n - 2] ^ ans[n - 1] ^ str[n - 1] ) == ans[0] &&
            ( ans[1] ^ ans[0] ^ str[0] ) == ans[n - 1] ) ok = true;
    } }

    if( ok == false )
        cout << -1 << endl;
    else {
        for( int i = 0; i < n; i ++ )
            cout << ( ans[i] == 0 ? 'S' : 'W' );
        cout << endl;
    }
    
    return 0;
}
### Prompt

Generate a Cpp solution to the following problem:

Snuke, who loves animals, built a zoo.

There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle. The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered N is adjacent to the animals numbered N-1 and 1.

There are two kinds of animals in this zoo: honest sheep that only speak the truth, and lying wolves that only tell lies.

Snuke cannot tell the difference between these two species, and asked each animal the following question: "Are your neighbors of the same species?" The animal numbered i answered s_i. Here, if s_i is `o`, the animal said that the two neighboring animals are of the same species, and if s_i is `x`, the animal said that the two neighboring animals are of different species.

More formally, a sheep answered `o` if the two neighboring animals are both sheep or both wolves, and answered `x` otherwise. Similarly, a wolf answered `x` if the two neighboring animals are both sheep or both wolves, and answered `o` otherwise.

Snuke is wondering whether there is a valid assignment of species to the animals that is consistent with these responses. If there is such an assignment, show one such assignment. Otherwise, print `-1`.

Constraints

* 3 ≤ N ≤ 10^{5}
* s is a string of length N consisting of `o` and `x`.

Input

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


N
s


Output

If there does not exist an valid assignment that is consistent with s, print `-1`. Otherwise, print an string t in the following format. The output is considered correct if the assignment described by t is consistent with s.

* t is a string of length N consisting of `S` and `W`.
* If t_i is `S`, it indicates that the animal numbered i is a sheep. If t_i is `W`, it indicates that the animal numbered i is a wolf.

Examples

Input

6
ooxoox


Output

SSSWWS


Input

3
oox


Output

-1


Input

10
oxooxoxoox


Output

SSWWSSSWWS

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int DIM = 1e5 + 5;

string str;
bool ans[DIM];

int main( void ) {
    
    int n;
    cin >> n >> str;
    
    for( char &ch : str )
        ch = ( ch == 'x' );
    
    bool ok = false;
    for( int v0 = 0; v0 <= 1 && ok == false; v0 ++ ) {
    for( int v1 = 0; v1 <= 1 && ok == false; v1 ++ ) {
        ans[0] = v0; ans[1] = v1;
        
        for( int i = 2; i < n; i ++ )
            ans[i] = ( ans[i - 2] ^ ans[i - 1] ^ str[i - 1] );
        
        if( ( ans[n - 2] ^ ans[n - 1] ^ str[n - 1] ) == ans[0] &&
            ( ans[1] ^ ans[0] ^ str[0] ) == ans[n - 1] ) ok = true;
    } }

    if( ok == false )
        cout << -1 << endl;
    else {
        for( int i = 0; i < n; i ++ )
            cout << ( ans[i] == 0 ? 'S' : 'W' );
        cout << endl;
    }
    
    return 0;
}
```