Problem:
Score : 300 points

Problem Statement

We have a string X, which has an even number of characters. Half the characters are S, and the other half are T.

Takahashi, who hates the string ST, will perform the following operation 10^{10000} times:

Among the occurrences of ST in X as (contiguous) substrings, remove the leftmost one. If there is no occurrence, do nothing.

Find the eventual length of X.

Constraints

2 ≦ |X| ≦ 200,000

The length of X is even.

Half the characters in X are S, and the other half are T.

Partial Scores

In test cases worth 200 points, |X| ≦ 200.

Input

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

X

Output

Print the eventual length of X.

Sample Input 1

TSTTSS

Sample Output 1

4

In the 1-st operation, the 2-nd and 3-rd characters of TSTTSS are removed.
X becomes TTSS, and since it does not contain ST anymore, nothing is done in the remaining 10^{10000}-1 operations.
Thus, the answer is 4.

Sample Input 2

SSTTST

Sample Output 2

0

X will eventually become an empty string: SSTTST ⇒ STST ⇒ ST ⇒ ``.

Sample Input 3

TSSTTTSS

Sample Output 3

4

X will become: TSSTTTSS ⇒ TSTTSS ⇒ TTSS.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.NoSuchElementException;

public class Main {
	private static void solve() {
		String s = nes();
		String prev;
		do {
			prev = s;
			s = s.replace("ST", "");
		} while (!prev.equals(s));
		out(s.length());
	}

	static BigInteger combination(int a, int b, BigInteger mod) {
		BigInteger q = BigInteger.ONE;
		BigInteger p = BigInteger.ONE;
		for (int i = a - b + 1; i <= a; i++) {
			q = q.multiply(BigInteger.valueOf(i)).mod(mod);
		}
		for (int j = 1; j <= b; j++) {
			p = p.multiply(BigInteger.valueOf(j)).mod(mod);
		}
		return q.multiply(p.modInverse(mod)).mod(mod);
	}

	static int abs(int x) {
		return x < 0 ? -x : x;
	}

	static int gcd(int x, int y) {
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		int z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(float val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(String.valueOf(val));
	}

	static String nes() {
		return IO.next();
	}

	static int nei() {
		return IO.nextInt();
	}

	static long nel() {
		return IO.nextLong();
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static int parseInt(char val) {
		return Integer.parseInt(String.valueOf(val));
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		solve();
		IO.flush();
	}
}

final class UnionFind {
	int[] data;

	UnionFind(int n) {
		data = new int[n];
		for (int i = 0; i < n; i++) {
			data[i] = -1;
		}
	}

	boolean union(int x, int y) {
		x = root(x);
		y = root(y);
		if (x == y)
			return false;
		if (data[y] < data[x]) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		data[x] += data[y];
		data[y] = x;
		return true;
	}

	boolean find(int x, int y) {
		return root(x) == root(y);
	}

	int root(int x) {
		return data[x] < 0 ? x : (data[x] = root(data[x]));
	}

	int size(int x) {
		return -data[root(x)];
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}