Chef recently took a course in linear algebra and learned about linear combinations of vectors. Therefore, in order to test his intelligence, Raj gave him a "fuzzy" problem to solve.
A sequence of integers $B_1, B_2, \ldots, B_M$ generates an integer $K$ if it is possible to find a sequence of integers $C_1, C_2, \ldots, C_M$ such that $C_1 \cdot B_1 + C_2 \cdot B_2 + \ldots + C_M \cdot B_M = K$.
In this problem, Chef has a sequence $A_1, A_2, \ldots, A_N$ and he should answer $Q$ queries. In each query, he is given an integer $K$; the answer to this query is the number of pairs $(l, r)$ such that $1 \le l \le r \le N$ and the subsequence $(A_l, A_{l+1}, \ldots, A_r)$ generates $K$.
Chef has no idea how to solve this problem ― can you help him find the answers to all queries?

-----Input-----
- The first line of the input contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains a single integer $Q$.
- The following $Q$ lines describe queries. Each of these lines contains a single integer $K$.

-----Output-----
For each query, print a single line containing one integer ― the number of contiguous subsequences that generate $K$.

-----Constraints-----
- $1 \le N, Q \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- $1 \le K \le 10^6$

-----Subtasks-----
Subtask #1 (10 points): $1 \le N \le 1,000$
Subtask #2 (90 points): original constraints

-----Example Input-----
2
2 4
3
1
2
8

-----Example Output-----
0
2
3

-----Explanation-----
The sequence $(2, 4)$ has three contiguous subsequences: $(2)$, $(4)$ and $(2, 4)$. 
- In the first query, $1$ cannot be generated by any subsequence.
- In the second query, $2$ is generated by subsequences $(2)$ and $(2, 4)$. For example, for the subsequence $(2, 4)$, we can choose $C_1 = 1$ and $C_2 = 0$.
- In the third query, $8$ is generated by all three subsequences.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import math as mt\nsz = 1000501\nn = int(input())\nx = [0]* sz\ngcs = [0]* int(n)\na = [int(temp) for temp in input().split()]\ngcs[n-1]=a[n-1]\ni=n-2\nwhile i>=0:\n gcs[i]=mt.gcd(gcs[i+1],a[i])\n i-=1\ni=0\nwhile i<n:\n curr = a[i]\n if curr < sz:\n  x[curr] += 1\n j=i+1\n while j<n:\n  curr = mt.gcd(curr,a[j])\n  if curr ==gcs[j]:\n   x[curr]+=(n-j)\n   break\n  elif curr<sz:\n   x[curr]+=1\n  j+=1\n i+=1\nq = int(input())\nfor i in range (q):\n q1=int(input())\n ans = 0\n for t in range(1, int(mt.sqrt(q1)+1)):\n  if q1%t ==0:\n   if q1/t==t:\n    ans += x[t]\n   else:\n    ans += x[t]\n    ans += x[int(q1/t)]\n print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 8010313