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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

using System.Runtime.CompilerServices;
using ll=System.Int64;

public class Contest
{
	static void Swap1<T>(ref T a, ref T b) { T t = a; a = b; b = t; }
	static void Swap2<T>(ref T a, ref T b) where T : IComparable { if (a.CompareTo(b)==1) Swap1(ref a, ref b); }  // b の方が小さければ交換
	static bool Chmin<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)== 1) { a = b; return true; } return false; }  // b の方が小さければ a を更新
	static bool Chmax<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)==-1) { a = b; return true; } return false; }  // b の方が大きければ a を更新
	static T[][] InitMat<T>(long len1, long len2, T val){ T[][] m = new T[len1][]; for (int i = 0; i < m.Length; i++) m[i] = Enumerable.Repeat(val, (int)len2).ToArray(); return m; }
	static T[][][] InitMat<T>(long len1, long len2, long len3, T val){ T[][][] m = new T[len1][][]; for (int i = 0; i < m.Length; i++) m[i] = InitMat(len2,len3,val); return m; }
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;

	public static void Main() {
		Solve_A();
 	}

	public static void Solve_A() {
		string s;
		MyIO.ReadMulti(out s);

		ll cnt = 0;
		ll ans = 0;
		for (int i = s.Length-1; 0<=i; i--)
		{
			if(s[i]=='S'){
				cnt++;
			}else{
				cnt--;
			}
			Chmax(ref ans, cnt);
		}

		MyIO.WriteMulti(ans*2);

	}
	public static void Solve_B() {
		ll  n;
		MyIO.ReadMulti(out n);
		VT<ll,ll>[] lrl;
		MyIO.ReadLines(n, out lrl);


		VT<ll,ll,ll>[] lri = new VT<ll, ll, ll>[n];
		for (int i = 0; i < n; i++)
		{
			lri[i] = new VT<ll, ll, ll>(lrl[i].Item1,lrl[i].Item2,i);
		}

		Array.Sort(lri,(x,y)=>(x.Item1.CompareTo(y.Item1)));

		VT<ll,ll>[] ll = new VT<ll, ll>[n+2];
		VT<ll,ll>[] rl = new VT<ll, ll>[n+2];
		ll[0]= new VT<ll, ll>(1,1000000000);
		rl[n+1]= new VT<ll, ll>(1,1000000000);

		long ans = 0;

/*
		for (int i = 1; i <= n; i++)
		{
			ll[i]= new VT<ll, ll>(Math.Max(lrl[i-1].Item1,ll[i-1].Item1),Math.Min(lrl[i-1].Item2,ll[i-1].Item2));
		}
		for (int i = (int)n; 0<i; i--)
		{
			rl[i]= new VT<ll, ll>(Math.Max(lrl[i-1].Item1,rl[i+1].Item1),Math.Min(lrl[i-1].Item2,rl[i+1].Item2));
		}

		for (int i = 1; i < n-1; i++)
		{
			ll v = ((ll[i].Item2>=ll[i].Item1)?(ll[i].Item2-ll[i].Item1+1):0) + ((rl[i+1].Item2>=rl[i+1].Item1)?(rl[i+1].Item2-rl[i+1].Item1+1):0);
			Chmax(ref ans, v);
		}
*/
		ll l2 = lri[n-1].Item1;
		ll r2 = lri[n-1].Item2;
		ll i2 = lri[n-1].Item3;
		ll i2a = lri[0].Item3;
		Array.Sort(lri,(x,y)=>(x.Item2.CompareTo(y.Item2)));		
		ll l1 = lri[0].Item1;
		ll r1 = lri[0].Item2;
		ll i1 = lri[0].Item3;
		if(i1==i2){
		 l1 = lri[1].Item1;
		 r1 = lri[1].Item2;
		 i1 = lri[1].Item3;
		}
		ll i1a = lri[n-1].Item3;


		if(i2a==i1a){
			for (int i = 0; i < n; i++)
			{
				if(lri[i].Item3==i1a) {
				l2 = lri[i].Item1;
				r2 = lri[i].Item2;
				}else{
				l1 = l1<lri[i].Item1?lri[i].Item1:l1;
				r1 = r1<lri[i].Item2?r1:lri[i].Item2;
				}
			}

		}else{
			for (int i = 0; i < n; i++)
			{
				ll tl1 = l1<lrl[i].Item1?lrl[i].Item1:l1;
				ll tl2 = l2<lrl[i].Item1?lrl[i].Item1:l2;
				ll tr1 = r1<lrl[i].Item2?r1:lrl[i].Item2;
				ll tr2 = r2<lrl[i].Item2?r2:lrl[i].Item2;
				ll d1 = Math.Max(r1-l1,-1)-Math.Max(tr1-tl1,-1);
				ll d2 = Math.Max(r2-l2,-1)-Math.Max(tr2-tl2,-1);
				if(d2<d1){
					l2 = tl2;
					r2 = tr2;
				}else{
					l1 = tl1;
					r1 = tr1;	
				}
			}


			}
			ans = Math.Max(r1-l1,-1)+Math.Max(r2-l2,-1)+2;
		MyIO.WriteMulti(ans);

	}
	public static void Solve_C() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_D() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_E() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_F() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}



	public static long Gcd(long a, long b) {
	    var v = new[] { a, b };
	    while (v[1] != 0) v = new[] { v[1], v[0] % v[1] };
	    return v[0];
	}









}


















#region MyIO

public struct VT<T, U>
{
	public T Item1; public U Item2;
    public VT(T a, U b) { Item1 = a; Item2 = b; }
}
public struct VT<T, U, V>
{
	public T Item1; public U Item2; public V Item3;
    public VT(T a, U b, V c) { Item1 = a; Item2 = b; Item3 = c; }
}
public struct VT<T, U, V, W>
{
	public T Item1; public U Item2; public V Item3; public W Item4;
    public VT(T a, U b, V c, W d) { Item1 = a; Item2 = b; Item3 = c; Item4 = d; }
}

public class Printer : System.IO.StreamWriter
{
	public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
	public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
}
public static class MyIO
{
	private static char[] splitter = new char[] {' '};
	private static bool eq<T, U>() => typeof(T).Equals(typeof(U));
	private static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
	private static T cv<T>(string s) =>
		eq<T, int>()    ? ct<T, int>(int.Parse(s))
	  : eq<T, long>()   ? ct<T, long>(long.Parse(s))
	  : eq<T, double>() ? ct<T, double>(double.Parse(s, System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T, char>()   ? ct<T, char>(s[0])
						: ct<T, string>(s);
			
	public static string[] ReadMulti<T>(out T a) {
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(ar[0]);
		return ar;
	}
	public static string[] ReadMulti<T, U>(out T a, out U b) {
		var ar = ReadMulti<T>(out a); 
        b = cv<U>(ar[1]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V>(out T a, out U b, out V c) {
		var ar = ReadMulti<T, U>(out a, out b); 
        c = cv<V>(ar[2]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W>(out T a, out U b, out V c, out W d) {
		var ar = ReadMulti<T, U, V>(out a, out b, out c); 
        d = cv<W>(ar[3]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e) {
		var ar = ReadMulti<T, U, V, W>(out a, out b, out c, out d); 
        e = cv<X>(ar[4]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f) {
		var ar = ReadMulti<T, U, V, W, X>(out a, out b, out c, out d, out e); 
        f = cv<Y>(ar[5]);
		return ar;
	}
	public static string[] ReadArray<T>(out T[] a) {		
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries);
		a = ar.Select(cv<T>).ToArray();
		return ar;
	}		
	public static string[][] ReadLines<T>(long n, out T[] a) {
		a = new T[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadMulti(out a[i]);
		return arr;
	}
	public static string[][] ReadLines<T, U>(long n, out VT<T, U>[] a) {
		a = new VT<T, U>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p;
			arr[i] = ReadMulti(out o, out p);
			a[i] = new VT<T, U>(o, p);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V>(long n, out VT<T, U, V>[] a) {
		a = new VT<T, U, V>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q;
			arr[i] = ReadMulti(out o, out p, out q);
			a[i] = new VT<T, U, V>(o, p, q);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V, W>(long n, out VT<T, U, V, W>[] a) {
		a = new VT<T, U, V, W>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q; W r;
			arr[i] = ReadMulti(out o, out p, out q, out r);
			a[i] = new VT<T, U, V, W>(o, p, q, r);
		}
		return arr;
	}
	public static string[][] ReadMatrix<T>(long n, out T[][] a) {
		a = new T[n][];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadArray(out a[i]);
		return arr;
	}

	private static void wwp(Action act){
		var sw = new Printer(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	private static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void WriteMulti(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length;i++) {
				string fs = wfm(a[i].GetType()) + ((i<a.Length-1) ? " " : Environment.NewLine);
				Console.Write(fs, a[i]);
			}
		});
	}
	public static void WriteArray<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T));
			string fs1 = fs + " ";
			string fs2 = fs + Environment.NewLine;
			for(int i=0;i<a.Length;i++) Console.Write( ((i<a.Length-1) ? fs1 : fs2), a[i]);
		});
	}
	public static void WriteLines<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T)) + Environment.NewLine;
			foreach(T x in a) Console.Write(fs, x);
		});
	}


}

#endregion