Problem: You are given a non-empty string s consisting of lowercase letters. Find the number of pairs of non-overlapping palindromic substrings of this string.

In a more formal way, you have to find the quantity of tuples (a, b, x, y) such that 1 ≤ a ≤ b < x ≤ y ≤ |s| and substrings s[a... b], s[x... y] are palindromes.

A palindrome is a string that can be read the same way from left to right and from right to left. For example, "abacaba", "z", "abba" are palindromes.

A substring s[i... j] (1 ≤ i ≤ j ≤ |s|) of string s = s1s2... s|s| is a string sisi + 1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac".

Input

The first line of input contains a non-empty string s which consists of lowercase letters ('a'...'z'), s contains at most 2000 characters.

Output

Output a single number — the quantity of pairs of non-overlapping palindromic substrings of s.

Please do not use the %lld format specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d format specifier.

Examples

Input

aa


Output

1


Input

aaa


Output

5


Input

abacaba


Output

36

Solution (in PYTHON):

Solution:
def do(l, r):
    n = len(r)
    lsum = [0]*n
    lsum[-1] = l[-1]

    for i in range(n-1, 0, -1):
        lsum[i-1] = lsum[i] + l[i-1]
    res = 0
    #print lsum

    for i in range(n-1):
        res += r[i]*lsum[i+1]

    return res 

def go():
    import sys
    t = sys.stdin.readline().rstrip()
    #t = "abacaba"
    #t = "aa"
    n = len(t)
    left_count = [0] * n
    right_count = [0] * n
    for u in range(n):
        i = 0
        while u + i < n and u - i >=0 and t[u+i] == t[u-i]:                 
                left_count[u-i] += 1
                right_count[u+i] += 1
                i += 1
        i = 1
        while  u + i - 1 < n and u - i >=0 and t[u+i-1] == t[u-i]:                 
                left_count[u-i] += 1
                right_count[u+i-1] += 1
                i += 1


    #print left_count, right_count

    print do(left_count, right_count)

go()