Problem: zscoder wants to generate an input file for some programming competition problem.

His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.

Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.

zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.

Input

The only line contains three integers n, x and y (1 ≤ n ≤ 107, 1 ≤ x, y ≤ 109) — the number of letters 'a' in the input file and the parameters from the problem statement.

Output

Print the only integer t — the minimum amount of time needed to generate the input file.

Examples

Input

8 1 1


Output

4


Input

8 1 10


Output

8

Solution (in JAVA):

Solution:

import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.*;

public class E {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int n = io.nextInt();
			long x = io.nextInt();
			long y = io.nextInt();
			SlideMinimum2 min = new SlideMinimum2(n+1);
			min.shift(0);
			long prev = 0;
			// dp[i] = dp[i-1] + x;
			// dp[i] = dp[j] + (2*j - i)*x + y
			for(int i = 1; i <= n; i++) {
				long v = prev + x;
				if(i > 1) {
					v = Math.min(v, min.min() - i * x + y);
				}
//				System.err.println(i + " " + (v + 2*i*x) + " " + min.min());
				if(i == n) {
					io.out.println(v);
				} else {
					prev = v;
					min.shift(v + 2*i*x);
				}
			}
		}
	}
	
	static
	public class SlideMinimum2 {
		private int s, t, idx;
		private long minValue;
		private int[] deq;
		private long[] a;

		public SlideMinimum2(int n) {
			idx = s = t = 0;
			minValue = Long.MAX_VALUE;
			a = new long[n];
			deq = new int[n];
		}

		// min [(idx+1)/2..idx)
		public long min() {
			return minValue;
		}

		public void shift(long val) {
			a[idx] = val;
			while(s < t && a[deq[t-1]] >= a[idx]) t--;
			deq[t++] = idx;
			while(idx > 0 && deq[s] * 2 < idx + 1) {
				s++;
			}
			minValue = a[deq[s]];
			idx++;
//			System.err.println(idx + " " + deq[s] + " " + min() + " " + Arrays.toString(deq));
		}
	}

	static
	class SegRMQLong {
		final long INF = 1L<<60;
		
		final int n;
		final long[] seg;
		final long[] add;
		
		public SegRMQLong(final int n) {
			this.n = Integer.highestOneBit(n) << 1;
			seg = new long[this.n << 1];
			add = new long[this.n << 1];
			Arrays.fill(seg, INF);
		}
		
		void propagate(int curL, int curR, int k) {
			if(add[k] != 0) {
				final int curM = (curL + curR) / 2;
				add(curL, curR, 2 * k + 1, add[k], curL, curM);
				add(curL, curR, 2 * k + 2, add[k], curM, curR);
				add[k] = 0;
			}
		}

		long get(int l, int r) { return get(l, r, 0, 0, n); }
		long get(int l, int r, int k, int curL, int curR) {
			if(curR <= l || curL >= r) return INF;
			if(l <= curL && curR <= r) { return seg[k]; }
			propagate(curL, curR, k);
			final int curM = (curL + curR) / 2;
			return Math.min(
					get(l, r, 2 * k + 1, curL, curM),
					get(l, r, 2 * k + 2, curM, curR));
		}

		void add(int l, int r, long v) { add(l, r, 0, v, 0, n); }
		void add(int l, int r, int k, long v, int curL, int curR) {
			if(curR <= l || curL >= r) return;
			if(l <= curL && curR <= r) { seg[k] += v; add[k] += v; return; }
			final int curM = (curL + curR) / 2;
			propagate(curL, curR, k);
			add(l, r, 2 * k + 1, v, curL, curM);
			add(l, r, 2 * k + 2, v, curM, curR);
			seg[k] = Math.min(seg[2*k+1], seg[2*k+2]);
		}
		
		void set(int i, long v) {
			// propagate to leaf
			add(i, i + 1, 0);
			
			i += n - 1;
			seg[i] = v;
			add[i] = 0;
			while(i != 0) {
				i = (i - 1) / 2;
				seg[i] = Math.min(seg[2*i+1], seg[2*i+2]) + add[i];
			}
		}
	}
	
	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }

	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new E().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}