This is the easy version of the problem. The only difference from the hard version is that in this version all coordinates are even.

There are n fence-posts at distinct coordinates on a plane. It is guaranteed that no three fence posts lie on the same line.

There are an infinite number of cows on the plane, one at every point with integer coordinates.

Gregor is a member of the Illuminati, and wants to build a triangular fence, connecting 3 distinct existing fence posts. A cow strictly inside the fence is said to be enclosed. If there are an odd number of enclosed cows and the area of the fence is an integer, the fence is said to be interesting.

Find the number of interesting fences.

Input

The first line contains the integer n (3 ≤ n ≤ 6000), the number of fence posts which Gregor can choose to form the vertices of a fence.

Each of the next n line contains two integers x and y (0 ≤ x,y ≤ 10^7, x and y are even), where (x,y) is the coordinate of a fence post. All fence posts lie at distinct coordinates. No three fence posts are on the same line.

Output

Print a single integer, the number of interesting fences. Two fences are considered different if they are constructed with a different set of three fence posts.

Examples

Input


3
0 0
2 0
0 4


Output


1


Input


5
0 0
2 16
30 14
4 6
2 10


Output


3

Note

In the first example, there is only 1 fence. That fence is interesting since its area is 4 and there is 1 enclosed cow, marked in red.

<image>

In the second example, there are 3 interesting fences. 

  * (0,0) — (30,14) — (2,10) 
  * (2,16) — (30,14) — (2,10) 
  * (30,14) — (4,6) — (2,10) 
20
200 716
88 526
434 134
996 890
718 220
820 462
614 178
848 208
724 536
124 710
408 228
846 606
222 32
642 180
694 964
438 994
718 524
688 692
126 494
102 116
 4
12 10
6 14
2 6
6 12

650
 2


def divisors(M):
    d=[]
    i=1
    while M>=i**2:
        if M%i==0:
            d.append(i)
            if i**2!=M:
                d.append(M//i)
        i=i+1
    return d

def popcount(x):
    x = x - ((x >> 1) & 0x55555555)
    x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
    x = (x + (x >> 4)) & 0x0f0f0f0f
    x = x + (x >> 8)
    x = x + (x >> 16)
    return x & 0x0000007f

def eratosthenes(n):
    res=[0 for i in range(n+1)]
    prime=set([])
    for i in range(2,n+1):
        if not res[i]:
            prime.add(i)
            for j in range(1,n//i+1):
                res[i*j]=1
    return prime

def factorization(n):
    res=[]
    for p in prime:
        if n%p==0:
            while n%p==0:
                n//=p
            res.append(p)
    if n!=1:
        res.append(n)
    return res

def euler_phi(n):
    res = n
    for x in range(2,n+1):
        if x ** 2 > n:
            break
        if n%x==0:
            res = res//x * (x-1)
            while n%x==0:
                n //= x
    if n!=1:
        res = res//n * (n-1)
    return res

def ind(b,n):
    res=0
    while n%b==0:
        res+=1
        n//=b
    return res

def isPrimeMR(n):
    d = n - 1
    d = d // (d & -d)
    L = [2, 3, 5, 7, 11, 13, 17]
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1: continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1: return 0
            t <<= 1
    return 1
def findFactorRho(n):
    from math import gcd
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g): return g
            elif isPrimeMR(n // g): return n // g
            return findFactorRho(g)
def primeFactor(n):
    i = 2
    ret = {}
    rhoFlg = 0
    while i*i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k: ret[i] = k
        i += 1 + i % 2
        if i == 101 and n >= 2 ** 20:
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    rhoFlg = 1
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k

    if n > 1: ret[n] = 1
    if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
    return ret

def divisors(n):
    res = [1]
    prime = primeFactor(n)
    for p in prime:
        newres = []
        for d in res:
            for j in range(prime[p]+1):
                newres.append(d*p**j)
        res = newres
    res.sort()
    return res

def xorfactorial(num):
    if num==0:
        return 0
    elif num==1:
        return 1
    elif num==2:
        return 3
    elif num==3:
        return 0
    else:
        x=baseorder(num)
        return (2**x)*((num-2**x+1)%2)+function(num-2**x)

def xorconv(n,X,Y):
    if n==0:
        res=[(X[0]*Y[0])%mod]
        return res
    x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
    y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
    z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
    w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
    res1=xorconv(n-1,x,y)
    res2=xorconv(n-1,z,w)
    former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
    latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
    former=list(map(lambda x:x%mod,former))
    latter=list(map(lambda x:x%mod,latter))
    return former+latter

def merge_sort(A,B):
    pos_A,pos_B = 0,0
    n,m = len(A),len(B)
    res = []
    while pos_A < n and pos_B < m:
        a,b = A[pos_A],B[pos_B]
        if a < b:
            res.append(a)
            pos_A += 1
        else:
            res.append(b)
            pos_B += 1
    res += A[pos_A:]
    res += B[pos_B:]
    return res

class UnionFindVerSize():
    def __init__(self, N):
        self._parent = [n for n in range(0, N)]
        self._size = [1] * N
        self.group = N

    def find_root(self, x):
        if self._parent[x] == x: return x
        self._parent[x] = self.find_root(self._parent[x])
        stack = [x]
        while self._parent[stack[-1]]!=stack[-1]:
            stack.append(self._parent[stack[-1]])
        for v in stack:
            self._parent[v] = stack[-1]
        return self._parent[x]

    def unite(self, x, y):
        gx = self.find_root(x)
        gy = self.find_root(y)
        if gx == gy: return

        self.group -= 1

        if self._size[gx] < self._size[gy]:
            self._parent[gx] = gy
            self._size[gy] += self._size[gx]
        else:
            self._parent[gy] = gx
            self._size[gx] += self._size[gy]

    def get_size(self, x):
        return self._size[self.find_root(x)]

    def is_same_group(self, x, y):
        return self.find_root(x) == self.find_root(y)

class WeightedUnionFind():
    def __init__(self,N):
        self.parent = [i for i in range(N)]
        self.size = [1 for i in range(N)]
        self.val = [0 for i in range(N)]
        self.flag = True
        self.edge = [[] for i in range(N)]

    def dfs(self,v,pv):
        stack = [(v,pv)]
        new_parent = self.parent[pv]
        while stack:
            v,pv = stack.pop()
            self.parent[v] = new_parent
            for nv,w in self.edge[v]:
                if nv!=pv:
                    self.val[nv] = self.val[v] + w
                    stack.append((nv,v))

    def unite(self,x,y,w):
        if not self.flag:
            return
        if self.parent[x]==self.parent[y]:
            self.flag = (self.val[x] - self.val[y] == w)
            return

        if self.size[self.parent[x]]>self.size[self.parent[y]]:
            self.edge[x].append((y,-w))
            self.edge[y].append((x,w))
            self.size[x] += self.size[y]
            self.val[y] = self.val[x] - w
            self.dfs(y,x)
        else:
            self.edge[x].append((y,-w))
            self.edge[y].append((x,w))
            self.size[y] += self.size[x]
            self.val[x] = self.val[y] + w
            self.dfs(x,y)

class Dijkstra():
    class Edge():
        def __init__(self, _to, _cost):
            self.to = _to
            self.cost = _cost

    def __init__(self, V):
        self.G = [[] for i in range(V)]
        self._E = 0
        self._V = V

    @property
    def E(self):
        return self._E

    @property
    def V(self):
        return self._V

    def add_edge(self, _from, _to, _cost):
        self.G[_from].append(self.Edge(_to, _cost))
        self._E += 1

    def shortest_path(self, s):
        import heapq
        que = []
        d = [10**15] * self.V
        d[s] = 0
        heapq.heappush(que, (0, s))

        while len(que) != 0:
            cost, v = heapq.heappop(que)
            if d[v] < cost: continue

            for i in range(len(self.G[v])):
                e = self.G[v][i]
                if d[e.to] > d[v] + e.cost:
                    d[e.to] = d[v] + e.cost
                    heapq.heappush(que, (d[e.to], e.to))
        return d

#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
    N = len(s)
    Z_alg = [0]*N

    Z_alg[0] = N
    i = 1
    j = 0
    while i < N:
        while i+j < N and s[j] == s[i+j]:
            j += 1
        Z_alg[i] = j
        if j == 0:
            i += 1
            continue
        k = 1
        while i+k < N and k + Z_alg[k]<j:
            Z_alg[i+k] = Z_alg[k]
            k += 1
        i += k
        j -= k
    return Z_alg

class BIT():
    def __init__(self,n,mod=0):
        self.BIT = [0]*(n+1)
        self.num = n
        self.mod = mod

    def query(self,idx):
        res_sum = 0
        mod = self.mod
        while idx > 0:
            res_sum += self.BIT[idx]
            if mod:
                res_sum %= mod
            idx -= idx&(-idx)
        return res_sum

    #Ai += x O(logN)
    def update(self,idx,x):
        mod = self.mod
        while idx <= self.num:
            self.BIT[idx] += x
            if mod:
                self.BIT[idx] %= mod
            idx += idx&(-idx)
        return

class dancinglink():
    def __init__(self,n,debug=False):
        self.n = n
        self.debug = debug
        self._left = [i-1 for i in range(n)]
        self._right = [i+1 for i in range(n)]
        self.exist = [True for i in range(n)]

    def pop(self,k):
        if self.debug:
            assert self.exist[k]
        L = self._left[k]
        R = self._right[k]
        if L!=-1:
            if R!=self.n:
                self._right[L],self._left[R] = R,L
            else:
                self._right[L] = self.n
        elif R!=self.n:
            self._left[R] = -1
        self.exist[k] = False

    def left(self,idx,k=1):
        if self.debug:
            assert self.exist[idx]
        res = idx
        while k:
            res = self._left[res]
            if res==-1:
                break
            k -= 1
        return res

    def right(self,idx,k=1):
        if self.debug:
            assert self.exist[idx]
        res = idx
        while k:
            res = self._right[res]
            if res==self.n:
                break
            k -= 1
        return res

class SparseTable():
    def __init__(self,A,merge_func,ide_ele):
        N=len(A)
        n=N.bit_length()
        self.table=[[ide_ele for i in range(n)] for i in range(N)]
        self.merge_func=merge_func

        for i in range(N):
            self.table[i][0]=A[i]

        for j in range(1,n):
            for i in range(0,N-2**j+1):
                f=self.table[i][j-1]
                s=self.table[i+2**(j-1)][j-1]
                self.table[i][j]=self.merge_func(f,s)

    def query(self,s,t):
        b=t-s+1
        m=b.bit_length()-1
        return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])

class BinaryTrie:
    class node:
        def __init__(self,val):
            self.left = None
            self.right = None
            self.max = val

    def __init__(self):
        self.root = self.node(-10**15)

    def append(self,key,val):
        pos = self.root
        for i in range(29,-1,-1):
            pos.max = max(pos.max,val)
            if key>>i & 1:
                if pos.right is None:
                    pos.right = self.node(val)
                    pos = pos.right
                else:
                    pos = pos.right
            else:
                if pos.left is None:
                    pos.left = self.node(val)
                    pos = pos.left
                else:
                    pos = pos.left
        pos.max = max(pos.max,val)

    def search(self,M,xor):
        res = -10**15
        pos = self.root
        for i in range(29,-1,-1):
            if pos is None:
                break

            if M>>i & 1:
                if xor>>i & 1:
                    if pos.right:
                        res = max(res,pos.right.max)
                    pos = pos.left
                else:
                    if pos.left:
                        res = max(res,pos.left.max)
                    pos = pos.right
            else:
                if xor>>i & 1:
                    pos = pos.right
                else:
                    pos = pos.left

        if pos:
            res = max(res,pos.max)
        return res

def solveequation(edge,ans,n,m):
    #edge=[[to,dire,id]...]
    x=[0]*m
    used=[False]*n
    for v in range(n):
        if used[v]:
            continue
        y = dfs(v)
        if y!=0:
            return False
    return x

    def dfs(v):
        used[v]=True
        r=ans[v]
        for to,dire,id in edge[v]:
            if used[to]:
                continue
            y=dfs(to)
            if dire==-1:
                x[id]=y
            else:
                x[id]=-y
            r+=y
        return r

class SegmentTree:
    def __init__(self, init_val, segfunc, ide_ele):
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.tree = [ide_ele] * 2 * self.num
        self.size = n
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        for i in range(self.num - 1, 0, -1):
            self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

    def update(self, k, x):
        k += self.num
        self.tree[k] = x
        while k > 1:
            self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
            k >>= 1

    def query(self, l, r):
        if r==self.size:
            r = self.num

        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.tree[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.tree[r - 1])
            l >>= 1
            r >>= 1
        return res

    def bisect_l(self,l,r,x):
        l += self.num
        r += self.num
        Lmin = -1
        Rmin = -1
        while l<r:
            if l & 1:
                if self.tree[l] <= x and Lmin==-1:
                    Lmin = l
                l += 1
            if r & 1:
                if self.tree[r-1] <=x:
                    Rmin = r-1
            l >>= 1
            r >>= 1

        if Lmin != -1:
            pos = Lmin
            while pos<self.num:
                if self.tree[2 * pos] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            return pos-self.num
        elif Rmin != -1:
            pos = Rmin
            while pos<self.num:
                if self.tree[2 * pos] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            return pos-self.num
        else:
            return -1

import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log

input = lambda :sys.stdin.buffer.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

n = int(input())
xy = [mi() for i in range(n)]
for i in range(n):
    x,y = xy[i]
    xy[i] = (x//2,y//2)

parity = [0 for i in range(4)]
for x,y in xy:
    p = 2 * (x&1) + (y&1)
    parity[p] += 1

res = 0
for i in range(n):
    for j in range(i+1,n):
        x0,y0 = xy[i]
        x1,y1 = xy[j]

        if (x0-x1)&1==0 and (y0-y1)&1==0:
            t = 0
        else:
            t = 1

        for p in range(4):
            x2 = p>>1 & 1
            y2 = p & 1

            tmp = t

            if (x0-x2)&1 or (y0-y2)&1:
                tmp += 1
            if (x1-x2)&1 or (y1-y2)&1:
                tmp += 1

            if tmp&1==0:
                plus = parity[p]
                if 2 * (x0&1) + (y0&1)==p:
                    plus -= 1
                if 2 * (x1&1) + (y1&1)==p:
                    plus -= 1
                res += plus

print(res//3)
