Parmida is a clever girl and she wants to participate in Olympiads this year. Of course she wants her partner to be clever too (although he's not)! Parmida has prepared the following test problem for Pashmak.

There is a sequence a that consists of n integers a1, a2, ..., an. Let's denote f(l, r, x) the number of indices k such that: l ≤ k ≤ r and ak = x. His task is to calculate the number of pairs of indicies i, j (1 ≤ i < j ≤ n) such that f(1, i, ai) > f(j, n, aj).

Help Pashmak with the test.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 106). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print a single integer — the answer to the problem.

Examples

Input

7
1 2 1 1 2 2 1


Output

8


Input

3
1 1 1


Output

1


Input

5
1 2 3 4 5


Output

0
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda: self.buffer.read().decode('ascii')
        self.readline = lambda: self.buffer.readline().decode('ascii')


def inp():
    return sys.stdin.readline().rstrip()


def mpint():
    return map(int, inp().split(' '))


def itg():
    return int(inp())


# ############################## import
class FenwickTree:
    def __init__(self, x=[]):
        """ transform list into BIT """
        self.bit = x
        for i in range(len(x)):
            j = i | (i + 1)
            if j < len(x):
                x[j] += x[i]

    def update(self, idx, x):
        """ updates bit[idx] += x """
        while idx < len(self.bit):
            self.bit[idx] += x
            idx |= idx + 1

    def query(self, end):
        """ calc sum(bit[:end]) """
        x = 0
        while end:
            x += self.bit[end - 1]
            end &= end - 1
        return x

    def findkth(self, k):
        """
        Find largest idx such that sum(x[:idx]) <= k
        all of the element in x have to be non-negative
        """
        idx = -1
        for d in reversed(range(len(self.bit).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(self.bit) and k >= self.bit[right_idx]:
                idx = right_idx
                k -= self.bit[idx]
        return idx + 1


# ############################## main
from collections import Counter


def solve():
    n = itg()
    arr = tuple(mpint())
    pre, suf = Counter(), Counter(arr)
    fi = [0] * n
    fj = [0] * n
    for i, a in enumerate(arr):
        pre[a] += 1
        fi[i] = pre[a]
        fj[i] = suf[a]
        suf[a] -= 1

    bit = FenwickTree([0] * (n + 1))
    ans = 0
    for i in reversed(range(n)):
        ans += bit.query(fi[i])
        bit.update(fj[i], 1)
    return ans


def main():
    # solve()
    print(solve())
    # for _ in range(itg()):
    #     print(solve())
    #     solve()
    # print("yes" if solve() else "no")
    # print("YES" if solve() else "NO")


DEBUG = 0
URL = 'https://codeforces.com/contest/459/problem/D'

if __name__ == '__main__':
    if DEBUG == 1:
        import requests  # ImportError: cannot import name 'md5' from 'sys' (unknown location)
        from ACgenerator.Y_Test_Case_Runner import TestCaseRunner

        runner = TestCaseRunner(main, URL)
        inp = runner.input_stream
        print = runner.output_stream
        runner.checking()
    elif DEBUG == 2:
        main()
    else:
        sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
        main()
# Please check!
