Problem: As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down will know and relocate him. 

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Thus, he came up with a puzzle to tell his mom his coordinates. His coordinates are the answer to the following problem.

A string consisting only of parentheses ('(' and ')') is called a bracket sequence. Some bracket sequence are called correct bracket sequences. More formally:

  * Empty string is a correct bracket sequence. 
  * if s is a correct bracket sequence, then (s) is also a correct bracket sequence. 
  * if s and t are correct bracket sequences, then st (concatenation of s and t) is also a correct bracket sequence. 



A string consisting of parentheses and question marks ('?') is called pretty if and only if there's a way to replace each question mark with either '(' or ')' such that the resulting string is a non-empty correct bracket sequence.

Will gave his mom a string s consisting of parentheses and question marks (using Morse code through the lights) and his coordinates are the number of pairs of integers (l, r) such that 1 ≤ l ≤ r ≤ |s| and the string slsl + 1... sr is pretty, where si is i-th character of s.

Joyce doesn't know anything about bracket sequences, so she asked for your help.

Input

The first and only line of input contains string s, consisting only of characters '(', ')' and '?' (2 ≤ |s| ≤ 5000).

Output

Print the answer to Will's puzzle in the first and only line of output.

Examples

Input

((?))


Output

4


Input

??()??


Output

7

Note

For the first sample testcase, the pretty substrings of s are:

  1. "(?" which can be transformed to "()". 
  2. "?)" which can be transformed to "()". 
  3. "((?)" which can be transformed to "(())". 
  4. "(?))" which can be transformed to "(())". 



For the second sample testcase, the pretty substrings of s are:

  1. "??" which can be transformed to "()". 
  2. "()". 
  3. "??()" which can be transformed to "()()". 
  4. "?()?" which can be transformed to "(())". 
  5. "??" which can be transformed to "()". 
  6. "()??" which can be transformed to "()()". 
  7. "??()??" which can be transformed to "()()()". 

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;
 
 
 
public class Main {
	
	static InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	
	static int oo = (int)1e9;
//	static long oo = (long)1e15;
	static int mod = 1_000_000_007;
//	static int mod = 998244353;
	
	static int[] di = {-1, 0, 1, 0};
	static int[] dj = {0, 1, 0, -1};
	
	static int M = 1000005;
	static double EPS = 1e-13;
	
	public static void main(String[] args) throws IOException {

		char[] a = in.readString().toCharArray();
		int n = a.length;
		int[][] b = new int[n][n];
		for(int i = 0; i < n; ++i) {
			int upper = 0;
			int lower = 0;
			for(int j = i; j < n; ++j) {
				if(a[j] == '(') {
					upper++;
					lower++;
				}
				else if(a[j] == ')') {
					upper--;
					lower--;
				}
				else {
					upper++;
					lower--;
				}
				if(upper < 0)
					break;
				int len = j - i + 1;
				if(len % 2 == 0 && lower <= 0)
					b[i][j]++;
			}
		}
		for(int j = n-1; j >= 0; --j) {
			int upper = 0;
			int lower = 0;
			for(int i = j; i >= 0; --i) {
				if(a[i] == '(') {
					upper++;
					lower++;
				}
				else if(a[i] == ')') {
					upper--;
					lower--;
				}
				else {
					upper++;
					lower--;
				}
				if(lower > 0)
					break;
				int len = j - i + 1;
				if(len % 2 == 0 && upper >= 0)
					b[i][j]++;
			}
		}
		int ans = 0;
		for(int i = 0; i < n; ++i) {
			for(int j = i; j < n; ++j) {
				if(b[i][j] == 2)
					ans++;
			}
		}
		System.out.println(ans);
		
		out.close();
	}
	
	
	static void update(int[] f, int i) {
		while(i < f.length) {
			f[i]++;
			i += (i & -i);
		}
	}
	
	static int query(int[] f, int i) {
		int ret = 0;
		while(i > 0) {
			ret += f[i];
			i -= (i & -i);
		}
		return ret;
	}
	
	static long invmod(long a, long mod) {
		BigInteger b = BigInteger.valueOf(a);
		BigInteger m = BigInteger.valueOf(mod);
		return b.modInverse(m).longValue();
	}
	
	
	static int find(int[] g, int x) {
		return g[x] = g[x] == x ? x : find(g, g[x]);
	}
	
	static void union(int[] g, int[] size, int x, int y) {
		x = find(g, x); y = find(g, y);
		if(x == y)
			return;
		if(size[x] < size[y]) {
			g[x] = y;
			size[y] += size[x];
		}
		else {
			g[y] = x;
			size[x] += size[y];
		}
	}
	
	static class Segment {
		Segment left, right;
		int size;
		int gcd;
//		int time, lazy;
		
		public Segment(int[] a, int l, int r) {
			super();
			if(l == r) {
				this.gcd = a[l];
				return;
			}
			int mid = (l + r) / 2;
			left = new Segment(a, l, mid);
			right = new Segment(a, mid+1, r);
			this.gcd = gcd(left.gcd, right.gcd);
		}
		
		boolean covered(int ll, int rr, int l, int r) {
			return ll <= l && rr >= r;
		}
		
		boolean noIntersection(int ll, int rr, int l, int r) {
			return ll > r || rr < l;
		}
		
//		void lazyPropagation() {
//			if(lazy != 0) {
//				if(left != null) {
//					left.setLazy(this.time, this.lazy);
//					right.setLazy(this.time, this.lazy);
//				}
//				else {
//					val = lazy;
//				}
//			}
//		}
		
//		void setLazy(int time, int lazy) {
//			if(this.time != 0 && this.time <= time)
//				return;
//			this.time = time;
//			this.lazy = lazy;
//		}
		
		
		int querySize(int ll, int rr, int l, int r) {
//			lazyPropagation();
			if(noIntersection(ll, rr, l, r))
				return 0;
			if(covered(ll, rr, l, r))
				return size;
			int mid = (l + r) / 2;
			int leftSize = left.querySize(ll, rr, l, mid);
			int rightSize = right.querySize(ll, rr, mid+1, r);
			return leftSize + rightSize;
		}
		
		int query(int k, int l, int r) {
			Segment trace = this;
			while(l < r) {
				int mid = (l + r) / 2;
				if(trace.left.size > k) {
					trace = trace.left;
					r = mid;
				}
				else {
					k -= trace.left.size;
					trace = trace.right;
					l = mid + 1;
				}
			}
			return l;
		}
		
		int queryCnt(int ll, int rr, int x, int l, int r) {
			if(noIntersection(ll, rr, l, r))
				return 0;
			if(covered(ll, rr, l, r)) {
				if(this.gcd % x == 0)
					return 0;
				if(l == r) {
					return 1;
				}
				int mid = (l + r) / 2;
				if(left.gcd % x != 0 && right.gcd % x != 0) {
					return 2;
				}
				if(left.gcd % x != 0) {
					return left.queryCnt(ll, rr, x, l, mid);
				}
				return right.queryCnt(ll, rr, x, mid+1, r);
			}
			int mid = (l + r) / 2;
			int leftCnt = left.queryCnt(ll, rr, x, l, mid);
			int rightCnt = right.queryCnt(ll, rr, x, mid+1, r);
			return leftCnt + rightCnt;
		}
		
		void update(int ll, int rr, int value, int l, int r) {
//			lazyPropagation();
			if(noIntersection(ll, rr, l, r))
				return;
			if(covered(ll, rr, l, r)) {
//				setLazy(time, knight);
				this.gcd = value;
				return;
			}
			int mid = (l + r) / 2;
			left.update(ll, rr, value, l, mid);
			right.update(ll, rr, value, mid+1, r);
			this.gcd = gcd(left.gcd, right.gcd);
		}
	}
	
	static long pow(long a, long n, long mod) {
		if(n == 0)
			return 1;
		if(n % 2 == 1)
			return a * pow(a, n-1, mod) % mod;
		long x = pow(a, n / 2, mod);
		return x * x % mod;
	}
	
	
	static int[] getPi(char[] a) {
		int m = a.length;
		int j = 0;
		int[] pi = new int[m];
		for(int i = 1; i < m; ++i) {
			while(j > 0 && a[i] != a[j])
				j = pi[j-1];
			if(a[i] == a[j]) {
				pi[i] = j + 1;
				j++;
			}
		}
		return pi;
	}
	
	static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}
	
	static BigInteger lcm2(long a, long b) {
		long g = gcd(a, b);
		BigInteger gg = BigInteger.valueOf(g);
		BigInteger aa = BigInteger.valueOf(a);
		BigInteger bb = BigInteger.valueOf(b);
		return aa.multiply(bb).divide(gg);
	}
	
	static boolean nextPermutation(int[] a) {
		for(int i = a.length - 2; i >= 0; --i) {
			if(a[i] < a[i+1]) {
				for(int j = a.length - 1; ; --j) {
					if(a[i] < a[j]) {
						int t = a[i];
						a[i] = a[j];
						a[j] = t;
						for(i++, j = a.length - 1; i < j; ++i, --j) {
							t = a[i];
							a[i] = a[j];
							a[j] = t;
						}
						return true;
					}
				}
			}
		}
		return false;
	}
	
	static void shuffle(Object[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			Object t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(int[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			int t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(long[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			long t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static int lower_bound(int[] a, int n, int k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	static int lower_bound(long[] a, int n, long k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	static BigInteger gcd(BigInteger a, BigInteger b) {
		return b.compareTo(BigInteger.ZERO) == 0 ? a : gcd(b, a.mod(b));
	}
	
	static class Pair implements Comparable<Pair> {
		int first, second;
 
		public Pair(int first, int second) {
			super();
			this.first = first;
			this.second = second;
		}
 
		@Override
		public int compareTo(Pair o) {
			return this.first != o.first ? this.first - o.first : this.second - o.second;
		}
		
//		@Override
//		public int compareTo(Pair o) {
//			return this.first != o.first ? o.first - this.first : o.second - this.second;
//		}
 
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}
 
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
	}
}
 
 
 
class InputReader {
 
	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 
	public InputReader(InputStream st) {
		this.stream = st;
	}
 
	public int read() {
		if (snumChars == -1)
			throw new InputMismatchException();
		if (curChar >= snumChars) {
			curChar = 0;
			try {
				snumChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (snumChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
 
	public int nextInt() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public long nextLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public int[] nextIntArray(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}
 
	public String readString() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
 
	public String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}
 
	public boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}
 
}