You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.

Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a. 

You can apply the following operations any number of times:

  * Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»); 
  * Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»). 



You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.

What is the minimum number of coins you need to spend to get a string consisting only of ones?

Input

The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).

The second line contains the string a of length n, consisting of zeros and ones.

Output

Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.

Examples

Input

5 1 10
01000


Output

11


Input

5 10 1
01000


Output

2


Input

7 2 3
1111111


Output

0

Note

In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5]. 

Then the string was changed as follows:

«01000» → «10000» → «11111».

The total cost of operations is 1 + 10 = 11.

In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5]. 

Then the string was changed as follows:

«01000» → «11000» → «11111».

The overall cost is 1 + 1 = 2.

In the third example, string already consists only of ones, so the answer is 0.
#include <bits/stdc++.h>
/*
#include<boost/multiprecision/cpp_int.hpp>
namespace mp=boost::multiprecision;
*/
using namespace std;
#define ll long long int
#define lo mp::cpp_int
#define pb push_back
#define pob pop_back
#define mk make_pair
#define endl "\n"
#define ce(x) cout << x <<"\n"
#define fill(s,v) memset(s,v,sizeof(s))
#define speed  { ios_base::sync_with_stdio(false); cin.tie(0); }
#define deb(x) cout<<#x<<" "<<x<<endl; 
#define INFINITE 1000000009
#define ull unsigned long long int
#define take(a,n) for(ll pp=0;pp<n;pp++) { cin>>a[pp]; }
#define take2(a,n) for(ll p=0;p<n;p++) { ll temp;cin>>temp;a.pb(temp); }
#define f(i,n) for(ll i=0;i<n;i++)
#define f1(i,a,n) for(ll i=a;i<n;i++)
#define show(a,n) for(ll p=0;p<n;p++) cout<<a[p]<<" ";
#define _ <<" "<<
#define nl cout<<endl;
#define sq(x) ((x)*(x))
#define call(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define ff first
#define ss second
#define lld long double
#define sc(n) scanf("%lld",&n);
#define de2(x,y) cout<<#x<<" = "<<(x) <<' '<< #y<<" = "<<y<<endl;typedef pair<int, int> pii;
#define copy(b,a,n) for(ll i=0;i<n;i++) b[i]=a[i];
#define clock() clock_out()
#define tc(tt) \
    ll tt;    \
    cin >> tt; \
    for (int _tt = 0; _tt < tt; _tt++) 
typedef vector<vector<ll>> matrix ;  
typedef pair<ll,ll> pii;
typedef vector<pii> vii;
typedef vector<ll> vi;   
const ll dx[4] = {-1, 0, 1, 0};
const ll dy[4] = {0, -1, 0, 1};
const ll mod = 1000000007;
ll gcd(ll a,ll b){if(!b)return a;return gcd(b,a%b);} 
ll power_mod(ll x,ll y,ll p){ll res=1;x%=p;while(y>0){if(y&1)res=(res*x)%p;y=y>>1;x=(x*x)%p;}return res;} 
ll modexpo(ll x,ll n,ll M){if(n==0)return 1;else if(n%2 == 0)return modexpo((x*x)%M,n/2,M);else return(x*modexpo((x*x)%M,(n-1)/2,M))%M;}
ll lcm(ll a, ll b){return (a*b)/gcd(a, b);}
ll sumofdigits(ll n){ll out=0;while(n){out+=(n%10);n/=10;}return out;}
bool isPrime(ll n){if (n <= 1)  
    return false; if (n <= 3)  return true; if (n%2 == 0 || n%3 == 0) return false; 
    for (ll i=5; i*i<=n; i=i+6) if (n%i == 0 || n%(i+2) == 0) return false;return true;} 
// ll power(ll a,ll b){if(b==0)return 1;if(b&1)return a*power(a,b-1);ll res=power(a,b/2);return res*res;}
ll bexpo(ll x,ll n){if(n==0)return 1;else if(n%2==0)return bexpo(x*x,n/2);else return x*bexpo(x*x,(n-1)/2);}
ll log(ll d){return log2(d);}
bool isPower(ll x, ll y){if(x==1) return (y==1); ll pow=1; while(pow<y) pow*=x; return(pow == y);}  
bool isPerfectSquare(long double x){long double sr = sqrt(x);return ((sr - floor(sr)) == 0);}   
bool compare(const pair<ll,ll> &a, const pair<ll,ll> &b) { return (a.second < b.second);} 
ll isPalindrome(string s){ll l=0;ll h=s.size()-1;while(h>l){if(s[l++]!=s[h--])return 0;}return 1;} 
ll setbits(ll n) { if(n==0)return 0; else return 1+setbits(n&(n-1)); } 
ll modInverse(ll A,ll M){return modexpo(A,M-2,M);}
ll suma(ll *a,ll n){ll sum=0;for(ll i=0;i<n;i++)sum+=a[i];return sum;}
// void clock_out(){
//   cerr<<"\nTime Elapsed : " << 1.0*clock() / CLOCKS_PER_SEC << " s\n";
// }
//------modular inverse by extended euclid-------//

// ll d, x, y;
// void extendedEuclid(ll A, ll B) {
//  if(B == 0) {
//  d = A;
//  x = 1;
//  y = 0;
//  }
//  else {
//  extendedEuclid(B, A%B);
//  ll temp = x;
//  x = y;
//  y = temp - (A/B)*y;
//  }
// }

// ll modInverse2(ll A, ll M){
// extendedEuclid(A,M);
// return (x%M+M)%M;
// }

//---------------------------------//

//---------------matrix exponentiation-------------------//

// matrix mul(matrix a,matrix b){
//   matrix res(n+1,vector<ll>(n+1));
//   f(i,n)f(j,n)f(k,n)res[i][j]=(res[i][j]%mod+((a[i][k]%mod)*(b[k][j]%mod))%mod)%mod;
//    return res;
// }
// matrix pow(matrix A,ll p) {
//     if(p==1) return A;
//     matrix res=pow(A,p/2) ;
//     res=mul(res,res);
//     if(p&1) res=mul(res,A) ;
//     return res;
// }

//-------------------------------------------------//

vector<ll> factorize(ll n) {
    vector<ll> res;
    for (ll i = 2; i * i <= n; ++i) {
        while (n % i == 0) {
            res.push_back(i);
            n /= i;
        }
    }
    if (n != 1) {
        res.push_back(n);
    }
    return res;
}

vector<ll> divisors(ll n){ 
    vector<ll> res;
    for (ll i=1; i<=sqrt(n); i++){ 
        if (n%i == 0){ if (n/i == i){ res.pb(i); } else{ res.pb(n/i); res.pb(i); } } 
    } 
    return res;
}   
vector<ll> primeFactors(ll n){  
    if(n==1) return vector<ll>(1,1);
    bool idx[1]={false};
    vector<ll> res;
    while (n%2 == 0){  
        if(!idx[1]){idx[1]=true;res.pb(2);}
        n = n/2;  
    }  
    for (ll i=3;i*i<=n; i+=2){
        bool once=false;
        while (n%i==0){ if(!once){res.pb(i);once=true;} n=n/i; }  
    }  
    if (n > 2)res.pb(n);
    return res;
}

//--------------------------------------------//

ll dxx[] = {1, 1, 0, -1, -1, -1, 0, 1};
ll dyy[] = {0, 1, 1, 1, 0, -1, -1, -1};

//----check if a point is in range-----///
///__builtin_ctz(x) --> get power of 2 dude !!!! 

bool check(ll x,ll y,ll n,ll m){return(x>=0&&x<n&&y>=0&&y<m);}

const int FULL_MASK = (1 << 10) - 1;
#define pi 3.1415926535897932

vector<vector<ll>> ed;

void bfs(ll s, vector<ll> &d) {
    d[s] = 0;
    queue<ll> q;
    q.push(s);
    while (!q.empty()) {
        ll v = q.front();
        q.pop();
        for (auto to : ed[v]) {
            if (d[to] == 1e9) {
                d[to] = d[v] + 1;
                q.push(to);
            }
        }
    }
} 
// void dfs(int u){
//     vis[u]=1;
//     // temp.push_back(u);
//     for(int i=0;i<adj[u].size();i++){
//         if(!vis[adj[u][i]])
//             dfs(adj[u][i]);
//     }
// }

// void dfs(ll u){
//     if(vis[u]) return;
//     deg += g[u].size();
//     ver++;
//     vis[u] = 1;
//     for(auto v: g[u])dfs(v);
// }
ll maxSubArraySum(ll a[],ll size) 
{ 
    ll max_so_far = a[0]; 
    ll curr_max = a[0]; 
  
   for (ll i = 1; i < size; i++) 
   { 
        curr_max = max(a[i], curr_max+a[i]); 
        max_so_far = max(max_so_far, curr_max); 
   } 
   return max_so_far; 
} 

struct node{
    ll a,b,c,d;
};

void solve(){
    ll n,x,y,i;string s;
    cin>>n>>x>>y>>s;
    ll c=0;
    i=0;
    while(i<n){
        while(s[i]=='1'&&i<n)i++;
        while(s[i]=='0'&&i<n)i++;
        if(i<n)c++;
    }
    if(s[i-1]=='0')c++;
    if(c==0){
        cout<<0;
        return;
    }
    ll mn=min(x,y);
    cout<<c*mn+y-mn;
}

int main(){
    // tc(tt){
        solve();
    // }
}

/*


*/