Problem:
Score : 400 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, arranged in a row in this order.

You can perform the following operation on this integer sequence any number of times:

Operation: Choose an integer i satisfying 1 \leq i \leq N-1. Multiply both A_i and A_{i+1} by -1.

Let B_1, B_2, ..., B_N be the integer sequence after your operations.

Find the maximum possible value of B_1 + B_2 + ... + B_N.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

-10^9 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value of B_1 + B_2 + ... + B_N.

Sample Input 1

3
-10 5 -4

Sample Output 1

19

If we perform the operation as follows:

Choose 1 as i, which changes the sequence to 10, -5, -4.

Choose 2 as i, which changes the sequence to 10, 5, 4.

we have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.

Sample Input 2

5
10 -4 -8 -11 3

Sample Output 2

30

Sample Input 3

11
-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000

Sample Output 3

10000000000

The output may not fit into a 32-bit integer type.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;

public class Main {

    public static void main(String[] args) {
	InputStream inputStream = System.in;
	OutputStream outputStream = System.out;
	MyInput in = new MyInput(inputStream);
	PrintWriter out = new PrintWriter(outputStream);
	TaskX solver = new TaskX();
	solver.solve(1, in, out);
	out.close();
    }

    static int INF = 1 << 30;
    static long LINF = 1L << 55;
    static int MOD = 1000000007;
    static int[] mh4 = { 0, -1, 1, 0 };
    static int[] mw4 = { -1, 0, 0, 1 };
    static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
    static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

    static class TaskX {

	public void solve(int testNumber, MyInput in, PrintWriter out) {

	    int n = in.nextInt();
	    long[] A = in.nextLongArray(n);
	    long ans = 0;
	    long min = LINF;
	    int cnt = 0;
	    for (long a : A) {
		ans += Math.abs(a);
		min = Math.min(min, Math.abs(a));
		if (a < 0) cnt++;
	    }

	    out.println(cnt % 2 == 1 ? ans -2 * min : ans);

	}
    }

    static class MyInput {
	private final BufferedReader in;
	private static int pos;
	private static int 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 MyInput(InputStream is) {
	    in = new BufferedReader(new InputStreamReader(is));
	}

	public int read() {
	    if (pos >= readLen) {
		pos = 0;
		try {
		    readLen = in.read(buffer);
		} catch (IOException e) {
		    throw new RuntimeException();
		}
		if (readLen <= 0) {
		    throw new MyInput.EndOfFileRuntimeException();
		}
	    }
	    return buffer[pos++];
	}

	public int nextInt() {
	    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() {
	    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() {
	    while (true) {
		final int c = read();
		if (!isSpace[c]) {
		    return (char) c;
		}
	    }
	}

	public String nextString() {
	    return new String(nextChars());
	}

	public char[] nextChars() {
	    int len = 0;
	    str[len++] = nextChar();
	    len = reads(len, isSpace);
	    return Arrays.copyOf(str, len);
	}

	public char[][] next2DChars(int h, int w) {
	    char[][] s = new char[h][w];
	    for (int i = 0; i < h; i++) {
		s[i] = nextChars();
	    }
	    return s;
	}

	int reads(int len, boolean[] accept) {
	    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 (MyInput.EndOfFileRuntimeException e) {
	    }
	    return len;
	}

	public int[] nextIntArray(final int n) {
	    final int[] res = new int[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextInt();
	    }
	    return res;
	}

	public int[] nextIntArray1Index(final int n) {
	    final int[] res = new int[n + 1];
	    for (int i = 1; i < n + 1; i++) {
		res[i] = nextInt();
	    }
	    return res;
	}

	public int[] nextIntArrayDec(final int n) {
	    final int[] res = new int[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextInt() - 1;
	    }
	    return res;
	}

	public long[] nextLongArray(final int n) {
	    final long[] res = new long[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextLong();
	    }
	    return res;
	}

	public long[] nextLongArray1Index(final int n) {
	    final long[] res = new long[n + 1];
	    for (int i = 1; i < n + 1; i++) {
		res[i] = nextLong();
	    }
	    return res;
	}

	public long[] nextLongArrayDec(final int n) {
	    final long[] res = new long[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextLong() - 1;
	    }
	    return res;
	}

	public double nextDouble() {
	    return Double.parseDouble(nextString());
	}

	public double[] nextDoubleArray(int n) {
	    double[] res = new double[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextDouble();
	    }
	    return res;
	}

	static class EndOfFileRuntimeException extends RuntimeException {
	}

    }
}