Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.Arrays;

/**
 * Support only ASCII code (8-bit char) for IO.
 */
public class Main {
	private static final int MOD = (int) 1E9 + 7;
	private static final int BUFFER_SIZE = (1 << 13);
	private static final int WHITE_SPACE = 32;
	private static final byte[] IN_BUFFER = new byte[BUFFER_SIZE];
	private static final byte[] OUT_BUFFER = new byte[BUFFER_SIZE];

	private int inNextByte;
	private int inNextIndex;
	private int inReadByteCount;
	private int outNextIndex;
	private InputStream in = System.in;
	private OutputStream out = System.out;
	private PrintStream err = System.err;

	private boolean showTrace;
	private boolean runOnEditor;
	private boolean inputFromLocal;
	private boolean outputToLocal;

	public Main(String[] args) {
		if (args != null) {
			if (args.length > 0) {
				showTrace = "1".equals(args[0].split(":")[1]);
			}
			if (args.length > 1) {
				runOnEditor = "1".equals(args[1].split(":")[1]);
			}
			if (args.length > 2) {
				inputFromLocal = "1".equals(args[2].split(":")[1]);
			}
			if (args.length > 3) {
				outputToLocal = "1".equals(args[3].split(":")[1]);
			}
		}
	}

	private void start() throws Exception {
		if (inputFromLocal) {
			char fs = File.separatorChar;
			String root = new File("").getAbsolutePath();
			String inPath = String.format("%s%c%s", root, fs, "in.txt");
			
			if (runOnEditor) {
				inPath = String.format("%s%c%s%c%s%c%s", root, fs, "src", fs, "testdata", fs, "in.txt");
			}
			if (showTrace) {
				err.println("Input: " + inPath);
			}

			in = new FileInputStream(inPath);
		}
		else if (showTrace) {
			err.println("Input: Console");
		}

		if (outputToLocal) {
			char fs = File.separatorChar;
			String root = new File("").getAbsolutePath();
			String outPath = String.format("%s%c%s", root, fs, "out.txt");
			
			if (runOnEditor) {
				outPath = String.format("%s%c%s%c%s%c%s", root, fs, "src", fs, "testdata", fs, "out.txt");
			}
			if (showTrace) {
				err.println("Output: " + outPath);
			}

			out = new FileOutputStream(outPath);
		}
		else if (showTrace) {
			err.println("Output: Console");
		}

		readByte();

		long start = 0;

		if (showTrace) {
			start = System.currentTimeMillis();
		}

		solve();
		in.close();
		flushOutBuf();

		if (showTrace) {
			err.printf("\nSolve completed in %.3f [s]\n", (System.currentTimeMillis() - start) / 1000.0);
		}
	}

	public static void main(String[] args) {
		try {
			new Main(args).start();
		}
		catch (Exception e) {
			e.printStackTrace();
		}
	}

	private int readByte() throws IOException {
		if (inNextIndex >= inReadByteCount) {
			inReadByteCount = in.read(IN_BUFFER, 0, BUFFER_SIZE);
			
			if (inReadByteCount == -1) {
				return (inNextByte = -1);
			}
			
			inNextIndex = 0;
		}

		return (inNextByte = IN_BUFFER[inNextIndex++]);
	}

	private char nc() throws IOException {
		while (inNextByte <= WHITE_SPACE) {
			readByte();
		}
		
		char res = (char) inNextByte;
		readByte();
		
		return res;
	}

	private int ni() throws IOException {
		int res = 0;
		
		while (inNextByte <= WHITE_SPACE) {
			readByte();
		}
		
		boolean minus = (inNextByte == '-');
		
		if (minus) {
			readByte();
		}
		if (inNextByte < '0' || inNextByte > '9') {
			throw new RuntimeException();
		}
		
		do {
			res = (res << 1) + (res << 3) + inNextByte - '0';
		}
		while (readByte() >= '0' && inNextByte <= '9');

		return minus ? -res : res;
	}

	private long nl() throws IOException {
		long res = 0;
		
		while (inNextByte <= WHITE_SPACE) {
			readByte();
		}
		
		boolean minus = (inNextByte == '-');
		
		if (minus) {
			readByte();
		}
		if (inNextByte < '0' || inNextByte > '9') {
			throw new RuntimeException();
		}
		
		do {
			res = (res << 1) + (res << 3) + inNextByte - '0';
		}
		while (readByte() >= '0' && inNextByte <= '9');

		return minus ? -res : res;
	}

	private double nd() throws IOException {
		double pre = 0.0, suf = 0.0, div = 1.0;
		
		while (inNextByte <= WHITE_SPACE) {
			readByte();
		}
		
		boolean minus = (inNextByte == '-');
		
		if (minus) {
			readByte();
		}
		if (inNextByte < '0' || inNextByte > '9') {
			throw new RuntimeException();
		}
		
		do {
			pre = 10 * pre + (inNextByte - '0');
		}
		while (readByte() >= '0' && inNextByte <= '9');

		if (inNextByte == '.') {
			while (readByte() >= '0' && inNextByte <= '9') {
				suf += (inNextByte - '0') / (div *= 10);
			}
		}

		return minus ? -(pre + suf) : (pre + suf);
	}

	private String ns() throws IOException {
		while (inNextByte <= WHITE_SPACE) {
			readByte();
		}

		StringBuilder sb = new StringBuilder();
		
		while (inNextByte > WHITE_SPACE) {
			sb.append((char) inNextByte);
			readByte();
		}
		
		return sb.toString();
	}

	private char[] nc(int n) throws IOException {
		char a[] = new char[n];
		
		for (int i = 0; i < n; ++i) {
			a[i] = nc();
		}
		
		return a;
	}

	private char[][] nc(int r, int c) throws IOException {
		char a[][] = new char[r][c];
		
		for (int i = 0; i < r; ++i) {
			a[i] = nc(c);
		}
		
		return a;
	}

	private int[] ni(int n) throws IOException {
		int a[] = new int[n];
		
		for (int i = 0; i < n; ++i) {
			a[i] = ni();
		}
		
		return a;
	}

	private int[][] ni(int r, int c) throws IOException {
		int a[][] = new int[r][c];
		
		for (int i = 0; i < r; ++i) {
			a[i] = ni(c);
		}
		
		return a;
	}

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

	private long[][] nl(int r, int c) throws IOException {
		long a[][] = new long[r][c];
		
		for (int i = 0; i < r; ++i) {
			a[i] = nl(c);
		}
		
		return a;
	}

	private double[] nd(int n) throws IOException {
		double a[] = new double[n];
		
		for (int i = 0; i < n; ++i) {
			a[i] = nd();
		}
		
		return a;
	}

	private double[][] nd(int r, int c) throws IOException {
		double a[][] = new double[r][c];
		
		for (int i = 0; i < r; ++i) {
			a[i] = nd(c);
		}
		
		return a;
	}

	private String[] ns(int n) throws IOException {
		String a[] = new String[n];
		
		for (int i = 0; i < n; ++i) {
			a[i] = ns();
		}
		
		return a;
	}

	private String[][] ns(int r, int c) throws IOException {
		String a[][] = new String[r][c];
		
		for (int i = 0; i < r; ++i) {
			a[i] = ns(c);
		}
		
		return a;
	}

	private void flushOutBuf() {
		try {
			if (outNextIndex <= 0) {
				return;
			}
			out.write(OUT_BUFFER, 0, outNextIndex);
			out.flush();
			outNextIndex = 0;
		}
		catch (Exception e) {
			e.printStackTrace();
		}
	}

	private void print(String s) {
		if (s == null) {
			s = "null";
		}
		for (int i = 0, N = s.length(); i < N; ++i) {
			OUT_BUFFER[outNextIndex++] = (byte) s.charAt(i);
			
			if (outNextIndex >= BUFFER_SIZE) {
				flushOutBuf();
			}
		}
	}

	private void println(String s) {
		print(s);
		print('\n');
	}

	private void print(Object obj) {
		if (obj == null) {
			print("null");
		}
		else {
			print(obj.toString());
		}
	}

	private void println(Object obj) {
		print(obj);
		print('\n');
	}

	private void print(String format, Object... args) {
		if (args != null) {
			format = String.format(format, args);
		}
		print(format);
	}

	private void println(String format, Object... args) {
		if (args != null) {
			format = String.format(format, args);
		}
		println(format);
	}

	private void solve() throws Exception {
		int N = ni();
		int[] arr = ni(N); // arr[i] are differ together

		Arrays.sort(arr);
		long cnt = 0;

		for (int x = 0, lastIndex = N - 1; x < lastIndex; ++x) {
			for (int y = x + 1; y < lastIndex; ++y) {
				int z = searchSmaller(arr, y + 1, lastIndex, arr[x] + arr[y]);

				if (z >= y + 1) {
					// Got: arr[z] < arr[x] + arr[y]
					// Then: y+1 -> z is good range
					cnt += z - y;
				}
			}
		}

		println(cnt);
	}

	private int searchSmaller(int[] arr, int fromIndex, int toIndex, int key) {
		if (arr[toIndex] < key) return toIndex;
		if (key <= arr[fromIndex]) return -1;

		// Got1: arr[fromIndex] < key <= arr[toIndex]
		// Got2: fromIndex is already good pos

		int midIndex;

		while (fromIndex < toIndex) {
			midIndex = (fromIndex + toIndex) / 2;

			if (key > arr[midIndex]) {
				fromIndex = midIndex + 1; // Must increase fromIndex
				// if proc stop at this time, we know fromIndex or fromIndex - 1 is expected pos
			}
			else if (key < arr[midIndex]) {
				toIndex = midIndex;
				// if proc stop at this time, we know midIndex (=fromIndex) - 1 is expected pos
			}
			else {
				return midIndex - 1;
			}
		}

		while (fromIndex >= 0 && arr[fromIndex] >= key) {
			--fromIndex;
		}

		return fromIndex;
	}
}

//javac Main.java & java Main showTrace:1 runOnEditor:0 inputFromLocal:1 outputToLocal:0
//javac Main.java ; java Main showTrace:1 runOnEditor:1 inputFromLocal:0 outputToLocal:0