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.
import javafx.util.Pair;
 
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.util.Map.Entry;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
 
public class abc {
		
		static int[][] graph;
		static int[] ans;
	
		public static void main(String[] args) throws Exception {
			// TODO Auto-generated method stub
			InputReader s = new InputReader(System.in);
			PrintWriter p = new PrintWriter(System.out);
			int n=s.nextInt();
			int x=s.nextInt();
			int y=s.nextInt();
			String str=s.nextLine();
			int i=0;
			int count=0;
			while(i<str.length()) {
				if(str.charAt(i)=='1') {
					i++;
					continue;
				}
				while(i<str.length() && str.charAt(i)=='0') {
					i++;
				}
				count++;
			}
			if(count==0) {
				System.out.println(0);
			}else {
				long ans=(count-1)*(long)Math.min(x, y);
				ans+=y;
				System.out.println(ans);
			}
			
		}
		
		
		
		
		
		
		
		static long power(long x, long y) 
	    { 
			long temp=0l; 
	        if( y == 0) 
	            return 1l; 
	        temp = power(x, y/2);  
	          
	        if (y%2 == 0) 
	            return temp*temp; 
	        else
	        { 
	            if(y > 0) 
	                return x * temp * temp; 
	            else
	                return (temp * temp) / x; 
	        } 
	    }  
		
		
		public static boolean helper(int[] arr1 , int[] arr2) {
			boolean[] temp=new boolean[3];
			if(arr1.length==0) return true;
			if(arr1[0]!=arr2[0]) return false;
			temp[arr1[0]+1]=true;
			for(int i=1 ; i<arr1.length ; i++) {
				
				if(arr1[i]==arr2[i]) {
					
				}else if(arr1[i]<arr2[i]) {
					if(!temp[2]) {
						return false;
					}
				}else {
					if(!temp[0]) {
						return false;
					}
				}
				temp[arr1[i]+1]=true;
			}
			return true;
		}
		
	
		public static ArrayList Divisors(long n) {
			ArrayList<Long> div = new ArrayList<>();
	 
			for (long i = 1; i <= Math.sqrt(n); i++) {
				if (n % i == 0) {
					div.add(i);
	 
					if (n / i != i)
						div.add(n / i);
				}
			}
			return div;
		}
	 
		public static int BinarySearch(long[] a, long k) {
			int n = a.length;
			int i = 0, j = n - 1;
			int mid = 0;
	 
			if (k < a[0])
				return 0;
			else if (k >= a[n - 1])
				return n;
			else {
				while (j - i > 1) {
					mid = (i + j) / 2;
	 
					if (k >= a[mid])
						i = mid;
					else
						j = mid;
				}
			}
	 
			return i + 1;
		}
	 
		public static long GCD(long a, long b) {
			if (b == 0)
				return a;
			else
				return GCD(b, a % b);
		}
	 
		public static long LCM(long a, long b) {
			return (a * b) / GCD(a, b);
		}
	 
		static class InputReader {
	 
			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;
	 
			public InputReader(InputStream stream) {
				this.stream = stream;
			}
	 
			public int snext() {
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) {
					curChar = 0;
					try {
						snumChars = stream.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			static class pair implements Comparable<pair> {
				Integer x, y;
	 
				pair(int x, int y) {
					this.x = x;
					this.y = y;
				}
	 
				public int compareTo(pair o) {
					int result = x.compareTo(o.x);
					if (result == 0)
						result = y.compareTo(o.y);
	 
					return result;
				}
	 
				public String toString() {
					return x + " " + y;
				}
	 
				public boolean equals(Object o) {
					if (o instanceof pair) {
						pair p = (pair) o;
						return p.x - x == 0 && p.y - y == 0;
					}
					return false;
				}
	 
				public int hashCode() {
					return new Long(x).hashCode() * 31 + new Long(y).hashCode();
				}
			}
	 
			public int nextInt() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public long nextLong() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int[] nextIntArray(int n) {
				int a[] = new int[n];
				for (int i = 0; i < n; i++) {
					a[i] = nextInt();
				}
				return a;
			}
	 
			public String readString() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public String nextLine() {
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(c));
				return res.toString();
			}
	 
			public boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	 
			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
	 
			public interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		}
	 
		static class CodeX {
			public static void sort(long arr[]) {
				merge_sort(arr, 0, arr.length - 1);
			}
	 
			private static void merge_sort(long A[], long start, long end) {
				if (start < end) {
					long mid = (start + end) / 2;
					merge_sort(A, start, mid);
					merge_sort(A, mid + 1, end);
					merge(A, start, mid, end);
				}
	 
			}
	 
			private static void merge(long A[], long start, long mid, long end) {
				long p = start, q = mid + 1;
				long Arr[] = new long[(int) (end - start + 1)];
				long k = 0;
	 
				for (int i = (int) start; i <= end; i++) {
					if (p > mid)
						Arr[(int) k++] = A[(int) q++];
	 
					else if (q > end)
						Arr[(int) k++] = A[(int) p++];
	 
					else if (A[(int) p] < A[(int) q])
						Arr[(int) k++] = A[(int) p++];
	 
					else
						Arr[(int) k++] = A[(int) q++];
				}
				for (int i = 0; i < k; i++) {
					A[(int) start++] = Arr[i];
				}
	 
			}
	 
		}
	 
	}

	
