1462_E1. Close Tuples (easy version)
This is the easy version of this problem. The only difference between easy and hard versions is the constraints on k and m (in this version k=2 and m=3). Also, in this version of the problem, you DON'T NEED to output the answer by modulo.

You are given a sequence a of length n consisting of integers from 1 to n. The sequence may contain duplicates (i.e. some elements can be equal).

Find the number of tuples of m = 3 elements such that the maximum number in the tuple differs from the minimum by no more than k = 2. Formally, you need to find the number of triples of indices i < j < z such that

$$$max(a_i, a_j, a_z) - min(a_i, a_j, a_z) ≤ 2.$$$

For example, if n=4 and a=[1,2,4,3], then there are two such triples (i=1, j=2, z=4 and i=2, j=3, z=4). If n=4 and a=[1,1,1,1], then all four possible triples are suitable.

Input

The first line contains a single integer t (1 ≤ t ≤ 2 ⋅ 10^5) — the number of test cases. Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the sequence a.

The next line contains n integers a_1, a_2,…, a_n (1 ≤ a_i ≤ n) — the sequence a.

It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.

Output

Output t answers to the given test cases. Each answer is the required number of triples of elements, such that the maximum value in the triple differs from the minimum by no more than 2. Note that in difference to the hard version of the problem, you don't need to output the answer by modulo. You must output the exact value of the answer.

Example

Input


4
4
1 2 4 3
4
1 1 1 1
1
1
10
5 6 1 3 2 9 8 1 2 4


Output


2
4
0
15
```python
    
#input = sys.stdin.readline   
import os 
import sys 
from io import BytesIO, IOBase  
import heapq as h 
import bisect 
 
from types import GeneratorType  
BUFSIZE = 8192
class SortedList: 
    def __init__(self, iterable=[], _load=200):
        """Initialize sorted list instance."""
        values = sorted(iterable)
        self._len = _len = len(values)
        self._load = _load
        self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)]
        self._list_lens = [len(_list) for _list in _lists]
        self._mins = [_list[0] for _list in _lists]
        self._fen_tree = []
        self._rebuild = True
 
    def _fen_build(self):
        """Build a fenwick tree instance."""
        self._fen_tree[:] = self._list_lens
        _fen_tree = self._fen_tree
        for i in range(len(_fen_tree)):
            if i | i + 1 < len(_fen_tree):
                _fen_tree[i | i + 1] += _fen_tree[i]
        self._rebuild = False
 
    def _fen_update(self, index, value):
        """Update `fen_tree[index] += value`."""
        if not self._rebuild:
            _fen_tree = self._fen_tree
            while index < len(_fen_tree):
                _fen_tree[index] += value
                index |= index+1
 
    def _fen_query(self, end):
        """Return `sum(_fen_tree[:end])`."""
        if self._rebuild:
            self._fen_build()
 
        _fen_tree = self._fen_tree
        x = 0
        while end:
            x += _fen_tree[end - 1]
            end &= end - 1
        return x
 
    def _fen_findkth(self, k):
        """Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`)."""
        _list_lens = self._list_lens
        if k < _list_lens[0]:
            return 0, k
        if k >= self._len - _list_lens[-1]:
            return len(_list_lens) - 1, k + _list_lens[-1] - self._len
        if self._rebuild:
            self._fen_build()
 
        _fen_tree = self._fen_tree
        idx = -1
        for d in reversed(range(len(_fen_tree).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
                idx = right_idx
                k -= _fen_tree[idx]
        return idx + 1, k
 
    def _delete(self, pos, idx):
        """Delete value at the given `(pos, idx)`."""
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens
 
        self._len -= 1
        self._fen_update(pos, -1)
        del _lists[pos][idx]
        _list_lens[pos] -= 1
 
        if _list_lens[pos]:
            _mins[pos] = _lists[pos][0]
        else:
            del _lists[pos]
            del _list_lens[pos]
            del _mins[pos]
            self._rebuild = True
 
    def _loc_left(self, value):
        """Return an index pair that corresponds to the first position of `value` in the sorted list."""
        if not self._len:
            return 0, 0
 
        _lists = self._lists
        _mins = self._mins
 
        lo, pos = -1, len(_lists) - 1
        while lo + 1 < pos:
            mi = (lo + pos) >> 1
            if value <= _mins[mi]:
                pos = mi
            else:
                lo = mi
 
        if pos and value <= _lists[pos - 1][-1]:
            pos -= 1
 
        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value <= _list[mi]:
                idx = mi
            else:
                lo = mi
 
        return pos, idx
 
    def _loc_right(self, value):
        """Return an index pair that corresponds to the last position of `value` in the sorted list."""
        if not self._len:
            return 0, 0
 
        _lists = self._lists
        _mins = self._mins
 
        pos, hi = 0, len(_lists)
        while pos + 1 < hi:
            mi = (pos + hi) >> 1
            if value < _mins[mi]:
                hi = mi
            else:
                pos = mi
 
        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value < _list[mi]:
                idx = mi
            else:
                lo = mi
 
        return pos, idx
 
    def add(self, value):
        """Add `value` to sorted list."""
        _load = self._load
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens
 
        self._len += 1
        if _lists:
            pos, idx = self._loc_right(value)
            self._fen_update(pos, 1)
            _list = _lists[pos]
            _list.insert(idx, value)
            _list_lens[pos] += 1
            _mins[pos] = _list[0]
            if _load + _load < len(_list):
                _lists.insert(pos + 1, _list[_load:])
                _list_lens.insert(pos + 1, len(_list) - _load)
                _mins.insert(pos + 1, _list[_load])
                _list_lens[pos] = _load
                del _list[_load:]
                self._rebuild = True
        else:
            _lists.append([value])
            _mins.append(value)
            _list_lens.append(1)
            self._rebuild = True
 
    def discard(self, value):
        """Remove `value` from sorted list if it is a member."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_right(value)
            if idx and _lists[pos][idx - 1] == value:
                self._delete(pos, idx - 1)
 
    def remove(self, value):
        """Remove `value` from sorted list; `value` must be a member."""
        _len = self._len
        self.discard(value)
        if _len == self._len:
            raise ValueError('{0!r} not in list'.format(value))
 
    def pop(self, index=-1):
        """Remove and return value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        value = self._lists[pos][idx]
        self._delete(pos, idx)
        return value
 
    def bisect_left(self, value):
        """Return the first index to insert `value` in the sorted list."""
        pos, idx = self._loc_left(value)
        return self._fen_query(pos) + idx
 
    def bisect_right(self, value):
        """Return the last index to insert `value` in the sorted list."""
        pos, idx = self._loc_right(value)
        return self._fen_query(pos) + idx
 
    def count(self, value):
        """Return number of occurrences of `value` in the sorted list."""
        return self.bisect_right(value) - self.bisect_left(value)
 
    def __len__(self):
        """Return the size of the sorted list."""
        return self._len
 
    def __getitem__(self, index):
        """Lookup value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        return self._lists[pos][idx]
 
    def __delitem__(self, index):
        """Remove value at `index` from sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        self._delete(pos, idx)
 
    def __contains__(self, value):
        """Return true if `value` is an element of the sorted list."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_left(value)
            return idx < len(_lists[pos]) and _lists[pos][idx] == value
        return False
 
    def __iter__(self):
        """Return an iterator over the sorted list."""
        return (value for _list in self._lists for value in _list)
 
    def __reversed__(self):
        """Return a reverse iterator over the sorted list."""
        return (value for _list in reversed(self._lists) for value in reversed(_list))
 
    def __repr__(self):
        """Return string representation of sorted list."""
        return 'SortedList({0})'.format(list(self))
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        import os
        self.os = os
        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 = self.os.read(self._fd, max(self.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 = self.os.read(self._fd, max(self.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:
            self.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")
 
import sys
from math import ceil,log2 
  
INT_MAX = sys.maxsize
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
import collections as col
import math, string
 
def getInts():
    return [int(s) for s in input().split()]
 
def getInt():
    return int(input())
 
def getStrs():
    return [s for s in input().split()]
 
def getStr():
    return input()
 
def listStr():
    return list(input())
def minVal(x, y) : 
    return x if (x < y) else y;  
  
# A utility function to get the  
# middle index from corner indexes.  
def getMid(s, e) : 
    return s + (e - s) // 2;  
  
""" A recursive function to get the  
minimum value in a given range  
of array indexes. The following  
are parameters for this function.  
  
    st --> Pointer to segment tree  
    index --> Index of current node in the  
        segment tree. Initially 0 is  
        passed as root is always at index 0  
    ss & se --> Starting and ending indexes  
                of the segment represented  
                by current node, i.e., st[index]  
    qs & qe --> Starting and ending indexes of query range """
def RMQUtil( st, ss, se, qs, qe, index) : 
  
    # If segment of this node is a part  
    # of given range, then return  
    # the min of the segment  
    if (qs <= ss and qe >= se) : 
        return st[index];  
  
    # If segment of this node  
    # is outside the given range  
    if (se < qs or ss > qe) : 
        return INT_MAX;  
  
    # If a part of this segment  
    # overlaps with the given range  
    mid = getMid(ss, se);  
    return minVal(RMQUtil(st, ss, mid, qs,  
                          qe, 2 * index + 1),  
                  RMQUtil(st, mid + 1, se, 
                          qs, qe, 2 * index + 2));  
  
# Return minimum of elements in range  
# from index qs (query start) to  
# qe (query end). It mainly uses RMQUtil()  
def RMQ( st, n, qs, qe) :  
  
    # Check for erroneous input values  
    if (qs < 0 or qe > n - 1 or qs > qe) : 
      
        print("Invalid Input");  
        return -1;  
      
    return RMQUtil(st, 0, n - 1, qs, qe, 0);  
  
# A recursive function that constructs  
# Segment Tree for array[ss..se].  
# si is index of current node in segment tree st  
def constructSTUtil(arr, ss, se, st, si) : 
  
    # If there is one element in array,  
    # store it in current node of  
    # segment tree and return  
    if (ss == se) : 
  
        st[si] = arr[ss];  
        return arr[ss];  
  
    # If there are more than one elements,  
    # then recur for left and right subtrees  
    # and store the minimum of two values in this node  
    mid = getMid(ss, se);  
    st[si] = minVal(constructSTUtil(arr, ss, mid, 
                                    st, si * 2 + 1), 
                    constructSTUtil(arr, mid + 1, se, 
                                    st, si * 2 + 2));  
      
    return st[si];  
  
"""Function to construct segment tree  
from given array. This function allocates  
memory for segment tree and calls constructSTUtil() 
to fill the allocated memory """
def constructST( arr, n) : 
  
    # Allocate memory for segment tree  
  
    # Height of segment tree  
    x = (int)(ceil(log2(n)));  
  
    # Maximum size of segment tree  
    max_size = 2 * (int)(2**x) - 1;  
   
    st = [0] * (max_size);  
  
    # Fill the allocated memory st  
    constructSTUtil(arr, 0, n - 1, st, 0);  
  
    # Return the constructed segment tree  
    return st;  
  
 
MOD = 10**9+7
mod=10**9+7
t=int(input())
#t=1
p=10**9+7
def ncr_util():
    
    inv[0]=inv[1]=1
    fact[0]=fact[1]=1
    for i in range(2,300001):
        inv[i]=(inv[i%p]*(p-p//i))%p
    for i in range(1,300001):
        inv[i]=(inv[i-1]*inv[i])%p
        fact[i]=(fact[i-1]*i)%p

def z_array(s1):
    n = len(s1)
    z=[0]*(n)
    l, r, k = 0, 0, 0
    for i in range(1,n): 
  
        # if i>R nothing matches so we will calculate. 
        # Z[i] using naive way. 
        if i > r: 
            l, r = i, i 
  
            # R-L = 0 in starting, so it will start 
            # checking from 0'th index. For example, 
            # for "ababab" and i = 1, the value of R 
            # remains 0 and Z[i] becomes 0. For string 
            # "aaaaaa" and i = 1, Z[i] and R become 5 
            while r < n and s1[r - l] == s1[r]: 
                r += 1
            z[i] = r - l 
            r -= 1
        else: 
  
            # k = i-L so k corresponds to number which 
            # matches in [L,R] interval. 
            k = i - l 
  
            # if Z[k] is less than remaining interval 
            # then Z[i] will be equal to Z[k]. 
            # For example, str = "ababab", i = 3, R = 5 
            # and L = 2 
            if z[k] < r - i + 1: 
                z[i] = z[k] 
  
            # For example str = "aaaaaa" and i = 2,  
            # R is 5, L is 0 
            else: 
  
                # else start from R and check manually 
                l = i 
                while r < n and s1[r - l] == s1[r]: 
                    r += 1
                z[i] = r - l 
         
                r -= 1  
    return z
'''
MAXN1=100001
spf=[0]*MAXN1

def sieve():
    spf[1]=1
    for i in range(2,MAXN1):
        spf[i]=i
    for i in range(4,MAXN1,2):
        spf[i]=2
    for i in range(3,math.ceil(math.sqrt(MAXN1))):
        if spf[i]==i:
            for j in range(i*i,MAXN1,i):
                if spf[j]==j:
                    spf[j]=i
    
def factor(x):
    d1={}
    x1=x
    while x!=1:
        d1[spf[x]]=d1.get(spf[x],0)+1
        x//=spf[x]
    return d1 
'''
def primeFactors(n): 
    d1={}  
    while n % 2 == 0: 
        d1[2]=d1.get(2,0)+1 
        n = n / 2
          
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            d1[i]=d1.get(i,0)+1 
            n = n // i 
              
    
    if n > 2: 
        d1[n]=d1.get(n,0)+1
    return d1
def fs(x):
    if x<2:
        return 0
        
    return (x*(x-1))//2
def solve():
    i=0
    j=0
    #print(123,l)
    cnt,ans=0,0
    while i<n-2:
        pos=bisect.bisect_left(l,l[i]+3)
        pos-=1
        #print(l,pos,pos-i,fs(pos-i))
       
        ans+=fs(pos-i)
        i+=1
    return ans
        
    
for _ in range(t):
    n=int(input())
    #d={}
    #n,m=map(int,input().split())
    #n=int(input())
    #s=input()
    #s2=input()
    l=list(map(int,input().split()))
    l.sort()
    #l2=list(map(int,input().split()))
    #l.sort()
    #l.sort(revrese=True)
    #x,y=(map(int,input().split()))
    #l=str(n)
    #l.sort(reverse=True)
    #l2.sort(reverse=True)
    #l1.sort(reverse=True)
    #(solve())
    print(solve())        
        
```