You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
'''                      __      __        __                  __    __        __  __       
                      /  |    /  |      /  |                /  |  /  |     /   |/| |      
  _______   ______   _$$ |_   $$ |____  $$ |____    ______  $$/   _$$ |_    $$/ |$$ |   __ 
 /       | /       / $$   |  $$         $$        /         /  | / $$   |   /  |$$ |  /  |
/$$$$$$$/ /$$$$$$  |$$$$$$/   $$$$$$$  |$$$$$$$  |/$$$$$$  |$$ | $$$$$$/   $$  |$$ |_/$$/ 
$$        $$    $$ |  $$ | __ $$ |  $$ |$$ |  $$ |$$ |  $$/ $$ |  $$ | __  $$  |$$   $$<  
 $$$$$$  |$$$$$$$$/   $$ |/  |$$ |  $$ |$$ |  $$ |$$ |      $$ |  $$ |/  | $$  |$$$$$$  \
/     $$/ $$       |  $$  $$/ $$ |  $$ |$$ |  $$ |$$ |      $$ |  $$  $$/  $$  |$$ | $$  |
$$$$$$$/   $$$$$$$/    $$$$/  $$/   $$/ $$/   $$/ $$/       $$/    $$$$/   $$/ |$$/   $$/ 
                                                                                        
'''                                                                                     
                                                                                        
import sys
from os import path
import bisect
if (path.exists('input.txt')):
    sys.stdin = open('input.txt', 'r')
    sys.stdout = open('output1.txt', 'w')
from heapq import heappop, heappush, heapify
from math import ceil
from collections import defaultdict
maxi = sys.maxsize
mini = -maxi
def countPairs(a, n):
    mp = defaultdict(int)
    a.sort(reverse = True)
    count = 0
    for i in range(n) :
        for j in range(32):
            count+=mp[(1<<j)-a[i]]
        mp[a[i]]+=1
    return count
 
n=int(input())
l=list(map(int,input().split()))
print(countPairs(l,n))