Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:

* He never visits a point with coordinate less than 0, or a point with coordinate greater than L.
* He starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.
* He only changes direction at a point with integer coordinate.



Each time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.

After Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:

* Put a stone in one of Snuke's ears.
* Remove a stone from one of Snuke's ears.



Find the minimum number of operations required when Ringo can freely decide how Snuke walks.

Constraints

* 1 \leq L \leq 2\times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq L)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


L
A_1
:
A_L


Output

Print the minimum number of operations required when Ringo can freely decide how Snuke walks.

Examples

Input

4
1
0
2
3


Output

1


Input

8
2
0
0
2
1
3
4
1


Output

3


Input

7
314159265
358979323
846264338
327950288
419716939
937510582
0


Output

1
import java.io.*;
import java.util.*;
import java.util.stream.*;

public class Main {
    private static InputStream is;
    private static PrintWriter out;
    private static String INPUT = "";

    long min(long... o) {
        return LongStream.of(o).min().getAsLong();
    }

    void solve() {
        int n = ni();
        long a[] = new long[n];
        for (int i = 0; i < n; ++i) {
            a[i] = nl();
        }
        long dp[][] = new long[n + 1][5];
        for (int i = 0; i <= n; ++i) Arrays.fill(dp[i], Long.MAX_VALUE / 2);
        dp[0][0] = 0;
        for (int i = 0; i < n; ++i) {
            dp[i + 1][0] = min(dp[i][0]) + a[i];
            dp[i + 1][1] = min(dp[i][0], dp[i][1]) + (a[i] == 0 ? 2 : a[i] % 2);
            dp[i + 1][2] = min(dp[i][0], dp[i][1], dp[i][2]) + (a[i] == 0 ? 1 : 1 - a[i] % 2);
            dp[i + 1][3] = min(dp[i][2], dp[i][3]) + (a[i] == 0 ? 2 : a[i] % 2);
            dp[i + 1][4] = min(dp[i][1], dp[i][2], dp[i][3], dp[i][4]) + a[i];
        }
        out.println(min(dp[n]));
    }

    public static void main(String[] args) throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        new Main().solve();
        out.flush();
    }

    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 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))) { // when nextLine, (isSpaceChar(b) && 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 long[] nal(int n) {
        long[] a = new long[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 class XorShift {
        int x = 123456789;
        int y = 362436069;
        int z = 521288629;
        int w = 88675123;

        int nextInt(int n) {
            final int t = x ^ (x << 11);
            x = y;
            y = z;
            z = w;
            w = (w ^ (w >>> 19)) ^ (t ^ (t >>> 8));
            final int r = w % n;
            return r < 0 ? r + n : r;
        }
    }

    private static void tr(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}