There are n armchairs, numbered from 1 to n from left to right. Some armchairs are occupied by people (at most one person per armchair), others are not. The number of occupied armchairs is not greater than n/2.

For some reason, you would like to tell people to move from their armchairs to some other ones. If the i-th armchair is occupied by someone and the j-th armchair is not, you can tell the person sitting in the i-th armchair to move to the j-th armchair. The time it takes a person to move from the i-th armchair to the j-th one is |i - j| minutes. You may perform this operation any number of times, but these operations must be done sequentially, i. e. you cannot tell a person to move until the person you asked to move in the last operation has finished moving to their destination armchair.

You want to achieve the following situation: every seat that was initially occupied must be free. What is the minimum time you need to do it?

Input

The first line contains one integer n (2 ≤ n ≤ 5000) — the number of armchairs.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1). a_i = 1 means that the i-th armchair is initially occupied, a_i = 0 means that it is initially free. The number of occupied armchairs is at most n/2.

Output

Print one integer — the minimum number of minutes you have to spend to achieve the following situation: every seat that was initially occupied must be free.

Examples

Input


7
1 0 0 1 0 0 1


Output


3


Input


6
1 1 1 0 0 0


Output


9


Input


5
0 0 0 0 0


Output


0

Note

In the first test, you can perform the following sequence:

  1. ask a person to move from armchair 1 to armchair 2, it takes 1 minute; 
  2. ask a person to move from armchair 7 to armchair 6, it takes 1 minute; 
  3. ask a person to move from armchair 4 to armchair 5, it takes 1 minute. 



In the second test, you can perform the following sequence:

  1. ask a person to move from armchair 1 to armchair 4, it takes 3 minutes; 
  2. ask a person to move from armchair 2 to armchair 6, it takes 4 minutes; 
  3. ask a person to move from armchair 4 to armchair 5, it takes 1 minute; 
  4. ask a person to move from armchair 3 to armchair 4, it takes 1 minute. 



In the third test, no seat is occupied so your goal is achieved instantly.
//package ecr109;
import java.io.*;
import java.util.*;

public class D {
	InputStream is;
	FastWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] a = na(n);
		List<Edge> es = new ArrayList<>();
		int src = n, sink = n+1;
		for(int i = 0;i < n;i++){
			if(a[i] == 1){
				es.add(new Edge(src, i, 1, 0));
			}else{
				es.add(new Edge(i, sink, 1, 0));
			}
			if(i+1 < n)es.add(new Edge(i, i+1, 9999, 1));
			if(i+1 < n)es.add(new Edge(i+1, i, 9999, 1));
		}
		long C = solveMinCostFlow(compileWD(sink+1, es), src, sink, n);
		out.println(C);
	}

	public static class Edge
	{
		public int from, to;
		public int capacity;
		public long cost;
		public int flow;
		public Edge complement;
		// public int iniflow;

		public Edge(int from, int to, int capacity, long cost) {
			this.from = from;
			this.to = to;
			this.capacity = capacity;
			this.cost = cost;
		}

		@Override
		public String toString() {
			return "Edge [from=" + from + ", to=" + to + ", capacity="
					+ capacity + ", cost=" + cost + "]";
		}
	}

	public static long addNegativeEdge(List<Edge> edges, Edge e, int src, int sink)
	{
		if(e.cost > 0){
			edges.add(e);
			return 0;
		}else{
			e.cost = -e.cost;
			edges.add(new Edge(src, e.to, e.capacity, 0));
			edges.add(new Edge(e.from, sink, e.capacity, 0));

			int d = e.from; e.from = e.to; e.to = d;
			edges.add(e);
			return (long)e.capacity * -e.cost;
		}
	}

	// TODO test
	public static long addMinCapacityConstraintEdge(List<Edge> edges, Edge e, int minCapacity, int src, int sink)
	{
		e.capacity -= minCapacity;
		edges.add(new Edge(src, e.to, minCapacity, 0));
		edges.add(new Edge(e.from, sink, minCapacity, 0));
		return (long)minCapacity * e.cost;
	}



	public static Edge[][] compileWD(int n, List<Edge> edges)
	{
		Edge[][] g = new Edge[n][];
		// cloning
		for(int i = edges.size()-1;i >= 0;i--){
			Edge origin = edges.get(i);
			Edge clone = new Edge(origin.to, origin.from, origin.capacity, -origin.cost);
			clone.flow = origin.capacity;
			clone.complement = origin;
			origin.complement = clone;
			edges.add(clone);
		}

		int[] p = new int[n];
		for(Edge e : edges)p[e.from]++;
		for(int i = 0;i < n;i++)g[i] = new Edge[p[i]];
		for(Edge e : edges)g[e.from][--p[e.from]] = e;
		return g;
	}

	public static class DQ {
		public int[] q;
		public int n;
		protected int pt, ph;

		public DQ(int n){ this.n = Integer.highestOneBit(n)<<1; q = new int[this.n]; pt = ph = 0; }

		public void addLast(int x){ q[ph] = x; ph = ph+1&n-1; }
		public void addFirst(int x){ pt = pt+n-1&n-1; q[pt] = x; }
		public int pollFirst(){ int ret = q[pt]; pt = pt+1&n-1; return ret; }
		public int pollLast(){ ph = ph+n-1&n-1; int ret = q[ph]; return ret; }
		public int getFirst(){ return q[pt]; }
		public int getFirst(int k){ return q[pt+k&n-1]; }
		public int getLast(){ return q[ph+n-1&n-1]; }
		public int getLast(int k){ return q[ph+n-k-1&n-1]; }
		public void clear(){ pt = ph = 0; }
		public int size(){ return ph-pt+n&n-1; }
		public boolean isEmpty(){ return ph==pt; }
	}

	public static class MinHeapL {
		public long[] a;
		public int[] map;
		public int[] imap;
		public int n;
		public int pos;
		public static long INF = Long.MAX_VALUE;

		public MinHeapL(int m)
		{
			n = Integer.highestOneBit((m+1)<<1);
			a = new long[n];
			map = new int[n];
			imap = new int[n];
			Arrays.fill(a, INF);
			Arrays.fill(map, -1);
			Arrays.fill(imap, -1);
			pos = 1;
		}

		public long add(int ind, long x)
		{
			int ret = imap[ind];
			if(imap[ind] < 0){
				a[pos] = x; map[pos] = ind; imap[ind] = pos;
				pos++;
				up(pos-1);
			}
			return ret != -1 ? a[ret] : x;
		}

		public long update(int ind, long x)
		{
			int ret = imap[ind];
			if(imap[ind] < 0){
				a[pos] = x; map[pos] = ind; imap[ind] = pos;
				pos++;
				up(pos-1);
			}else{
				a[ret] = x;
				up(ret);
				down(ret);
			}
			return x;
		}

		public long remove(int ind)
		{
			if(pos == 1)return INF;
			if(imap[ind] == -1)return INF;

			pos--;
			int rem = imap[ind];
			long ret = a[rem];
			map[rem] = map[pos];
			imap[map[pos]] = rem;
			imap[ind] = -1;
			a[rem] = a[pos];
			a[pos] = INF;
			map[pos] = -1;

			up(rem);
			down(rem);
			return ret;
		}

		public long min() { return a[1]; }
		public int argmin() { return map[1]; }
		public int size() {	return pos-1; }

		private void up(int cur)
		{
			for(int c = cur, p = c>>>1;p >= 1 && a[p] > a[c];c>>>=1, p>>>=1){
				long d = a[p]; a[p] = a[c]; a[c] = d;
				int e = imap[map[p]]; imap[map[p]] = imap[map[c]]; imap[map[c]] = e;
				e = map[p]; map[p] = map[c]; map[c] = e;
			}
		}

		private void down(int cur)
		{
			for(int c = cur;2*c < pos;){
				int b = a[2*c] < a[2*c+1] ? 2*c : 2*c+1;
				if(a[b] < a[c]){
					long d = a[c]; a[c] = a[b]; a[b] = d;
					int e = imap[map[c]]; imap[map[c]] = imap[map[b]]; imap[map[b]] = e;
					e = map[c]; map[c] = map[b]; map[b] = e;
					c = b;
				}else{
					break;
				}
			}
		}
	}

	public static long solveMinCostFlow(Edge[][] g, int source, int sink, long all)
	{
		int n = g.length;
		long mincost = 0;
		long[] potential = new long[n];

		final long[] d = new long[n];
		MinHeapL q = new MinHeapL(n);
		while(all > 0){
			// shortest path src->sink
			Edge[] inedge = new Edge[n];
			Arrays.fill(d, Long.MAX_VALUE / 2);
			d[source] = 0;
			q.add(source, 0);
			while(q.size() > 0){
				int cur = q.argmin();
				q.remove(cur);
				for(Edge ne : g[cur]){
					if(ne.capacity - ne.flow > 0){
						long nd = d[cur] + ne.cost + potential[cur] - potential[ne.to];
						if(d[ne.to] > nd){
							inedge[ne.to] = ne;
							d[ne.to] = nd;
							q.update(ne.to, nd);
						}
					}
				}
			}

			if(inedge[sink] == null)break;

			long minflow = all;
			long sumcost = 0;
			for(Edge e = inedge[sink];e != null;e = inedge[e.from]){
				if(e.capacity - e.flow < minflow)minflow = e.capacity - e.flow;
				sumcost += e.cost;
			}
			mincost += minflow * sumcost;
			for(Edge e = inedge[sink];e != null;e = inedge[e.from]){
				e.flow += minflow;
				e.complement.flow -= minflow;
			}

			all -= minflow;
			for(int i = 0;i < n;i++){
				potential[i] += d[i];
			}
		}
		return mincost;
	}


	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private 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 boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}

	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}

	private 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 int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}

	private int ni() { return (int)nl(); }

	private 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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
