Vasya has a sequence $a$ consisting of $n$ integers $a_1, a_2, \dots, a_n$. Vasya may pefrom the following operation: choose some number from the sequence and swap any pair of bits in its binary representation. For example, Vasya can transform number $6$ $(\dots 00000000110_2)$ into $3$ $(\dots 00000000011_2)$, $12$ $(\dots 000000001100_2)$, $1026$ $(\dots 10000000010_2)$ and many others. Vasya can use this operation any (possibly zero) number of times on any number from the sequence.

Vasya names a sequence as good one, if, using operation mentioned above, he can obtain the sequence with bitwise exclusive or of all elements equal to $0$.

For the given sequence $a_1, a_2, \ldots, a_n$ Vasya'd like to calculate number of integer pairs $(l, r)$ such that $1 \le l \le r \le n$ and sequence $a_l, a_{l + 1}, \dots, a_r$ is good.


-----Input-----

The first line contains a single integer $n$ ($1 \le n \le 3 \cdot 10^5$) — length of the sequence.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^{18}$) — the sequence $a$.


-----Output-----

Print one integer — the number of pairs $(l, r)$ such that $1 \le l \le r \le n$ and the sequence $a_l, a_{l + 1}, \dots, a_r$ is good.


-----Examples-----
Input
3
6 7 14

Output
2

Input
4
1 2 1 16

Output
4



-----Note-----

In the first example pairs $(2, 3)$ and $(1, 3)$ are valid. Pair $(2, 3)$ is valid since $a_2 = 7 \rightarrow 11$, $a_3 = 14 \rightarrow 11$ and $11 \oplus 11 = 0$, where $\oplus$ — bitwise exclusive or. Pair $(1, 3)$ is valid since $a_1 = 6 \rightarrow 3$, $a_2 = 7 \rightarrow 13$, $a_3 = 14 \rightarrow 14$ and $3 \oplus 13 \oplus 14 = 0$.

In the second example pairs $(1, 2)$, $(2, 3)$, $(3, 4)$ and $(1, 4)$ are valid.

Source: codeforces | Difficulty: HARD
Tags: Dynamic programming

Bit manipulation


Solutions:
from bisect import bisect_left
n = int(input())
b = list(map(int, input().split()))
pre = [0]
res = []
for j in range(n):
	res.append(bin(b[j]).count('1'))
	pre.append(pre[-1] + res[-1])
ans = 0
e = 1
o = 0
for j in range(n):
	if pre[j + 1] % 2 == 0:
		ans += e
		e += 1
	else:
		ans += o
		o += 1
	s = 0
	m = 0
	i = j
	while i >= max(0, j - 62):
		s += res[i]
		m = max(m, res[i])
		if s % 2 == 0 and s < 2 * m:
			ans += -1
		i += -1
print(ans)


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')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')
from math import factorial
from collections import Counter, defaultdict, deque
from heapq import heapify, heappop, heappush

def RL():
	return map(int, sys.stdin.readline().rstrip().split())

def RLL():
	return list(map(int, sys.stdin.readline().rstrip().split()))

def N():
	return int(input())

def comb(n, m):
	return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0

def perm(n, m):
	return factorial(n) // factorial(n - m) if n >= m else 0

def mdis(x1, y1, x2, y2):
	return abs(x1 - x2) + abs(y1 - y2)
mod = 998244353
INF = float('inf')

def main():
	n = N()
	arr = RLL()
	narr = [bin(i).count('1') for i in arr]
	res = 0
	dp = [[0, 0] for _ in range(n + 1)]
	dp[0][0] = 1
	sm = [0]
	for i in narr:
		sm.append(sm[-1] + i)
	for i in range(1, n + 1):
		t = res
		if i > 1:
			if sm[i] % 2:
				res += dp[i - 2][1]
			else:
				res += dp[i - 2][0]
		dp[i][sm[i] % 2] = dp[i - 1][sm[i] % 2] + 1
		dp[i][sm[i] % 2 ^ 1] = dp[i - 1][sm[i] % 2 ^ 1]
	for l in range(1, n + 1):
		ma = narr[l - 1]
		for r in range(l + 1, min(n + 1, l + 63)):
			ma = max(ma, narr[r - 1])
			now = sm[r] - sm[l - 1]
			if now % 2 == 0 and ma > now - ma:
				res -= 1
	print(res)
main()


import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))
b = [0] * n
for i in range(n):
	ai = a[i]
	for j in range(61):
		if ai >> j & 1:
			b[i] += 1
cnt = [[0] * (n + 1) for i in range(2)]
cnt[0][n] = 1
res = 0
suf = 0
for i in range(n)[::-1]:
	s = 0
	MAX = 0
	add = 0
	for j in range(i, n):
		if j - i >= 65:
			break
		s += b[j]
		MAX = max(MAX, b[j])
		if MAX > s - MAX and s % 2 == 0:
			add -= 1
	suf += b[i]
	add += cnt[suf & 1][i + 1]
	res += add
	cnt[0][i] = cnt[0][i + 1]
	cnt[1][i] = cnt[1][i + 1]
	if suf & 1:
		cnt[1][i] += 1
	else:
		cnt[0][i] += 1
print(res)


N = int(input())
a = list(map(int, input().split()))
cnt = [[0] * (N + 1) for i in range(2)]
b = [0] * N
for i in range(N):
	b[i] = bin(a[i]).count('1')
num = 0
suf = 0
cnt[0][N] = 1
for i in range(N - 1, -1, -1):
	s = 0
	ma = 0
	suf += b[i]
	num += cnt[suf & 1][i + 1]
	for j in range(i, min(N, i + 65)):
		s += b[j]
		ma = max(ma, b[j])
		if ma * 2 > s and s % 2 == 0:
			num -= 1
	cnt[0][i] = cnt[0][i + 1]
	cnt[1][i] = cnt[1][i + 1]
	if suf & 1:
		cnt[1][i] += 1
	else:
		cnt[0][i] += 1
print(num)


import os
import sys
from math import *
from collections import *
from bisect import *
from io import BytesIO, IOBase

def vsInput():
	sys.stdin = open('input.txt', 'r')
	sys.stdout = open('output.txt', 'w')
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')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')
ALPHA = 'abcdefghijklmnopqrstuvwxyz'
M = 998244353
EPS = 1e-06

def Ceil(a, b):
	return a // b + int(a % b > 0)

def value():
	return tuple(map(int, input().split()))

def array():
	return [int(i) for i in input().split()]

def Int():
	return int(input())

def Str():
	return input()

def arrayS():
	return [i for i in input().split()]

def setBit(x):
	ans = 0
	while x:
		x = x & x - 1
		ans += 1
	return ans
n = Int()
a = [setBit(i) for i in array()]
have = [1, 0]
ans = 0
cur = 0
prev = 0
for i in range(n):
	cur += a[i]
	ans += have[cur % 2]
	have[cur % 2] += 1
	j = 0
	ma = -1
	temp = 0
	while i - j >= 0 and j < 100:
		temp += a[i - j]
		ma = max(ma, a[i - j])
		ans -= temp % 2 == 0 and ma * 2 > temp
		j += 1
print(ans)


n = int(input())
a = list(map(int, input().split()))
for i in range(n):
	x = bin(a[i])
	a[i] = x.count('1')
even = 0
odd = 0
cnt = 0
sofar = 0
for i in range(n):
	sofar += a[i]
	if sofar % 2:
		odd += 1
	else:
		even += 1
even += 1
sofar = 0
for i in range(n):
	if sofar % 2:
		odd -= 1
		cnt += odd
	else:
		even -= 1
		cnt += even
	sofar += a[i]
for i in range(n):
	sum1 = 0
	max1 = a[i]
	for j in range(i, min(i + 100, n)):
		sum1 += a[j]
		max1 = max(max1, a[j])
		if sum1 % 2 == 0 and sum1 < 2 * max1:
			cnt -= 1
print(cnt)


n = int(input())
cnt = [[0 for _ in range(n + 1)] for _ in range(2)]
b = [bin(_).count('1') for _ in list(map(int, input().split()))]
res = 0
suf_sum = 0
cnt[0][n] = 1
for i in range(n)[::-1]:
	(_sum, mx) = (0, 0)
	lst_j = i
	add = 0
	for j in range(i, min(n, i + 65)):
		_sum += b[j]
		mx = max(mx, b[j])
		if mx > _sum - mx and _sum % 2 == 0:
			add -= 1
		lst_j = j
	suf_sum += b[i]
	add += cnt[suf_sum & 1][i + 1]
	res += add
	cnt[0][i] = cnt[0][i + 1]
	cnt[1][i] = cnt[1][i + 1]
	if suf_sum & 1:
		cnt[1][i] += 1
	else:
		cnt[0][i] += 1
print(res)


import sys

def rint():
	return list(map(int, sys.stdin.readline().split()))

def get_num1(i):
	cnt = 0
	while i:
		if i % 2:
			cnt += 1
		i //= 2
	return cnt
n = int(input())
a = list(rint())
b = [get_num1(aa) for aa in a]
ans = 0
S0 = [0] * n
S0[0] = b[0] % 2
for i in range(1, n):
	S0[i] = (S0[i - 1] + b[i]) % 2
even_cnt = S0.count(0)
ans = even_cnt
for i in range(1, n):
	if b[i - 1] % 2:
		even_cnt = n - i - even_cnt
	else:
		even_cnt -= 1
	ans += even_cnt
for i in range(n):
	max_value = 0
	sum_value = 0
	for j in range(1, 62):
		if i + j > n:
			break
		sum_value += b[i + j - 1]
		max_value = max(max_value, b[i + j - 1])
		if 2 * max_value > sum_value and sum_value % 2 == 0:
			ans -= 1
print(ans)


import os
import sys
import math
from io import BytesIO, IOBase
from fractions import Fraction
import collections
from itertools import permutations
from collections import defaultdict
from collections import deque
import threading
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')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class SegmentTree1:

	def __init__(self, data, default=10 ** 6, func=lambda a, b: min(a, b)):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)
MOD = 10 ** 9 + 7

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD
mod = 10 ** 9 + 7
omod = 998244353
prime = [True for i in range(10)]
pp = [0] * 10

def SieveOfEratosthenes(n=10):
	p = 2
	c = 0
	while p * p <= n:
		if prime[p] == True:
			c += 1
			for i in range(p, n + 1, p):
				pp[i] += 1
				prime[i] = False
		p += 1

def binarySearch(arr, n, key):
	left = 0
	right = n - 1
	mid = 0
	res = arr[n - 1]
	while left <= right:
		mid = (right + left) // 2
		if arr[mid] >= key:
			res = arr[mid]
			right = mid - 1
		else:
			left = mid + 1
	return res

def binarySearch1(arr, n, key):
	left = 0
	right = n - 1
	mid = 0
	res = arr[0]
	while left <= right:
		mid = (right + left) // 2
		if arr[mid] > key:
			right = mid - 1
		else:
			res = arr[mid]
			left = mid + 1
	return res
n = int(input())
cnt = [[0 for _ in range(n + 1)] for _ in range(2)]
b = [bin(_).count('1') for _ in list(map(int, input().split()))]
res = 0
suf_sum = 0
cnt[0][n] = 1
for i in range(n)[::-1]:
	(_sum, mx) = (0, 0)
	lst_j = i
	add = 0
	for j in range(i, min(n, i + 65)):
		_sum += b[j]
		mx = max(mx, b[j])
		if mx > _sum - mx and _sum % 2 == 0:
			add -= 1
		lst_j = j
	suf_sum += b[i]
	add += cnt[suf_sum & 1][i + 1]
	res += add
	cnt[0][i] = cnt[0][i + 1]
	cnt[1][i] = cnt[1][i + 1]
	if suf_sum & 1:
		cnt[1][i] += 1
	else:
		cnt[0][i] += 1
print(res)


from array import array

def popcount(x):
	res = 0
	while x > 0:
		res += x & 1
		x >>= 1
	return res

def main():
	n = int(input())
	a = array('i', [popcount(int(x)) for x in input().split(' ')])
	(ans, s0, s1) = (0, 0, 0)
	for i in range(n):
		if a[i] & 1:
			(s0, s1) = (s1, s0 + 1)
		else:
			(s0, s1) = (s0 + 1, s1)
		ans += s0
	for i in range(n):
		(mx, sum) = (a[i], 0)
		for j in range(i, min(n, i + 70)):
			mx = max(mx, a[j] << 1)
			sum += a[j]
			if sum & 1 is 0 and mx > sum:
				ans -= 1
	print(ans)
main()