AtCoDeer the deer found N rectangle lying on the table, each with height 1. If we consider the surface of the desk as a two-dimensional plane, the i-th rectangle i(1≤i≤N) covers the vertical range of [i-1,i] and the horizontal range of [l_i,r_i], as shown in the following figure:

<image>

AtCoDeer will move these rectangles horizontally so that all the rectangles are connected. For each rectangle, the cost to move it horizontally by a distance of x, is x. Find the minimum cost to achieve connectivity. It can be proved that this value is always an integer under the constraints of the problem.

Constraints

* All input values are integers.
* 1≤N≤10^5
* 1≤l_i<r_i≤10^9

Input

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


N
l_1 r_1
l_2 r_2
:
l_N r_N


Output

Print the minimum cost to achieve connectivity.

Examples

Input

3
1 3
5 7
1 3


Output

2


Input

3
2 5
4 6
1 4


Output

0


Input

5
999999999 1000000000
1 2
314 315
500000 500001
999999999 1000000000


Output

1999999680


Input

5
123456 789012
123 456
12 345678901
123456 789012
1 23


Output

246433


Input

1
1 400


Output

0
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni();
		int[][] co = new int[n][];
		for(int i = 0;i < n;i++){
			co[i] = new int[]{ni(), ni()};
		}
		
		long ret = 0;
		SimpleMinHeapL upper = new SimpleMinHeapL(n+1);
		SimpleMinHeapL lower = new SimpleMinHeapL(n+1);
		long uoffset = 0;
		long loffset = 0;
		upper.add(co[0][0]);
		lower.add(-co[0][0]);
		for(int i = 1;i < n;i++){
			loffset -= co[i][1]-co[i][0];
			uoffset += co[i-1][1]-co[i-1][0];
			long L = -lower.min() + loffset;
			long R = upper.min() + uoffset;
			if(co[i][0] < L){
				ret += L - co[i][0];
			}
			if(co[i][0] > R){
				ret += co[i][0] - R;
			}
			if(co[i][0] <= L){
				lower.add(-(co[i][0]-loffset));
				lower.add(-(co[i][0]-loffset));
				while(upper.size() != lower.size()){
					long v = -lower.poll() + loffset;
					upper.add(v-uoffset);
				}
			}else{
				upper.add(co[i][0]-uoffset);
				upper.add(co[i][0]-uoffset);
				while(upper.size() != lower.size()){
					long v = upper.poll() + uoffset;
					lower.add(-(v-loffset));
				}
			}
		}
		out.println(ret);
	}
	
	public static class SimpleMinHeapL {
		public long[] a;
		public int n;
		public int pos;
		public static final long INF = Long.MAX_VALUE;
		
		public SimpleMinHeapL(int m)
		{
			n = m+1;
			a = new long[n];
			Arrays.fill(a, INF);
			pos = 1;
		}
		
		public SimpleMinHeapL(long[] in)
		{
			n = in.length+1;
			if((n&1)==1)n++;
			a = new long[n];
			pos = 1+in.length;
//			Arrays.fill(a, INF);
			a[0] = a[n-1] = a[n-2] = INF;
			System.arraycopy(in, 0, a, 1, in.length);
			for(int t = pos/2-1;t >= 1;t--){
				for(int c = t;2*c < pos;){
					int smaller = a[2*c] < a[2*c+1] ? 2*c : 2*c+1;
					if(a[smaller] < a[c]){
						long d = a[c]; a[c] = a[smaller]; a[smaller] = d;
						c = smaller;
					}else{
						break;
					}
				}
			}
		}
		
		public void add(long x)
		{
			a[pos++] = x;
			for(int c = pos-1, p = c>>>1;p >= 1 && a[c] < a[p];c>>>=1, p>>>=1){
				long d = a[p]; a[p] = a[c]; a[c] = d;
			}
		}
		
		public long poll()
		{
			if(pos == 1)return INF;
			pos--;
			long ret = a[1];
			a[1] = a[pos];
			a[pos] = INF;
			for(int c = 1;2*c < pos;){
				int smaller = a[2*c] < a[2*c+1] ? 2*c : 2*c+1;
				if(a[smaller] < a[c]){
					long d = a[c]; a[c] = a[smaller]; a[smaller] = d;
					c = smaller;
				}else{
					break;
				}
			}
			return ret;
		}
		
		public long min() { return a[1]; }
		public int size() { return pos-1; }
	}
	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
