In this problem, we will deal with binary strings. Each character of a binary string is either a 0 or a 1. We will also deal with substrings; recall that a substring is a contiguous subsequence of a string. We denote the substring of string $s$ starting from the $l$-th character and ending with the $r$-th character as $s[l \dots r]$. The characters of each string are numbered from $1$.

We can perform several operations on the strings we consider. Each operation is to choose a substring of our string and replace it with another string. There are two possible types of operations: replace 011 with 110, or replace 110 with 011. For example, if we apply exactly one operation to the string 110011110, it can be transformed into 011011110, 110110110, or 110011011.

Binary string $a$ is considered reachable from binary string $b$ if there exists a sequence $s_1$, $s_2$, ..., $s_k$ such that $s_1 = a$, $s_k = b$, and for every $i \in [1, k - 1]$, $s_i$ can be transformed into $s_{i + 1}$ using exactly one operation. Note that $k$ can be equal to $1$, i. e., every string is reachable from itself.

You are given a string $t$ and $q$ queries to it. Each query consists of three integers $l_1$, $l_2$ and $len$. To answer each query, you have to determine whether $t[l_1 \dots l_1 + len - 1]$ is reachable from $t[l_2 \dots l_2 + len - 1]$.


-----Input-----

The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of string $t$.

The second line contains one string $t$ ($|t| = n$). Each character of $t$ is either 0 or 1.

The third line contains one integer $q$ ($1 \le q \le 2 \cdot 10^5$) — the number of queries.

Then $q$ lines follow, each line represents a query. The $i$-th line contains three integers $l_1$, $l_2$ and $len$ ($1 \le l_1, l_2 \le |t|$, $1 \le len \le |t| - \max(l_1, l_2) + 1$) for the $i$-th query.


-----Output-----

For each query, print either YES if $t[l_1 \dots l_1 + len - 1]$ is reachable from $t[l_2 \dots l_2 + len - 1]$, or NO otherwise. You may print each letter in any register.


-----Example-----
Input
5
11011
3
1 3 3
1 4 2
1 2 3

Output
Yes
Yes
No

Difficulty: HARD

Starter code:

Solutions:
import sys
input = sys.stdin.readline
MOD = 987654103
n = int(input())
t = input()
place = []
f1 = []
e1 = []
s = []
curr = 0
count1 = 0
for i in range(n):
	c = t[i]
	if c == '0':
		if count1:
			e1.append(i - 1)
			if count1 & 1:
				s.append(1)
				curr += 1
				e1.append(-1)
				f1.append(-1)
			count1 = 0
		else:
			f1.append(-1)
			e1.append(-1)
		place.append(curr)
		curr += 1
		s.append(0)
	else:
		if count1 == 0:
			f1.append(i)
		count1 += 1
		place.append(curr)
if count1:
	if count1 & 1:
		s.append(1)
	else:
		s.append(0)
	curr += 1
	e1.append(n - 1)
	e1.append(-1)
	f1.append(-1)
place.append(curr)
pref = [0]
val = 0
for i in s:
	val *= 3
	val += i + 1
	val %= MOD
	pref.append(val)
q = int(input())
out = []
for _ in range(q):
	(l1, l2, leng) = map(int, input().split())
	l1 -= 1
	l2 -= 1
	starts = (l1, l2)
	hashes = []
	for start in starts:
		end = start + leng - 1
		smap = place[start]
		emap = place[end]
		if t[end] == '1':
			emap -= 1
		if s[smap] == 1:
			smap += 1
		prep = False
		app = False
		if t[start] == '1':
			last = e1[place[start]]
			last = min(last, end)
			count = last - start + 1
			if count % 2:
				prep = True
		if t[end] == '1':
			first = f1[place[end]]
			first = max(first, start)
			count = end - first + 1
			if count % 2:
				app = True
		preHash = 0
		length = 0
		if smap <= emap:
			length = emap - smap + 1
			preHash = pref[emap + 1]
			preHash -= pref[smap] * pow(3, emap - smap + 1, MOD)
			preHash %= MOD
		if length == 0 and prep and app:
			app = False
		if prep:
			preHash += pow(3, length, MOD) * 2
			length += 1
		if app:
			preHash *= 3
			preHash += 2
		preHash %= MOD
		hashes.append(preHash)
	if hashes[0] == hashes[1]:
		out.append('Yes')
	else:
		out.append('No')
print('\n'.join(out))


import sys
input = sys.stdin.readline
n = int(input())
t = input().strip()
q = int(input())
ZEROS = [0] * n
ZERO_ONE = []
ONECOUNT = [0] * n
ind = 0
count = 0
for i in range(n):
	ZEROS[i] = ind
	if t[i] == '0':
		ind += 1
		ONECOUNT[i] = count % 2
		ZERO_ONE.append(count % 2)
		count = 0
	else:
		count += 1
		ONECOUNT[i] = count
ZEROS.append(ind)
S = ZERO_ONE
LEN = len(S)
p = 2
import random
mod = random.randint(10 ** 8, 10 ** 9) * 2 + 1
mod2 = random.randint(10 ** 8, 10 ** 9) * 2 + 1
mod3 = random.randint(10 ** 8, 10 ** 9) * 2 + 1
mod4 = random.randint(10 ** 8, 10 ** 9) * 2 + 1
TABLE = [0]
TABLE2 = [0]
TABLE3 = [0]
TABLE4 = [0]
for i in range(LEN):
	TABLE.append(p * TABLE[-1] % mod + S[i] % mod)
	TABLE2.append(p * TABLE2[-1] % mod2 + S[i] % mod2)
	TABLE3.append(p * TABLE3[-1] % mod3 + S[i] % mod2)
	TABLE4.append(p * TABLE4[-1] % mod4 + S[i] % mod4)

def hash_ij(i, j):
	return (TABLE[j] - TABLE[i] * pow(p, j - i, mod)) % mod

def hash_ij2(i, j):
	return (TABLE2[j] - TABLE2[i] * pow(p, j - i, mod2)) % mod2

def hash_ij3(i, j):
	return (TABLE3[j] - TABLE3[i] * pow(p, j - i, mod3)) % mod3

def hash_ij4(i, j):
	return (TABLE4[j] - TABLE4[i] * pow(p, j - i, mod4)) % mod4

def zcount(l, LEN):
	return ZEROS[l + LEN] - ZEROS[l]

def first_check(l, LEN):
	if t[l] == '0':
		return 0
	else:
		return (ZERO_ONE[ZEROS[l]] - ONECOUNT[l] + 1) % 2

def equalcheck(l1, l2, LEN):
	(f1, f2) = (ZEROS[l1] + 1, ZEROS[l2] + 1)
	if l1 + LEN - 1 == '0':
		la1 = ZEROS[l1 + LEN]
	else:
		la1 = ZEROS[l1 + LEN] - 1
	if l2 + LEN - 1 == '0':
		la2 = ZEROS[l2 + LEN]
	else:
		la2 = ZEROS[l2 + LEN] - 1
	if hash_ij(f1, la1 + 1) == hash_ij(f2, la2 + 1) and hash_ij2(f1, la1 + 1) == hash_ij2(f2, la2 + 1) and (hash_ij3(f1, la1 + 1) == hash_ij3(f2, la2 + 1)) and (hash_ij4(f1, la1 + 1) == hash_ij4(f2, la2 + 1)):
		return 'Yes'
	else:
		return 'No'
for queries in range(q):
	(l1, l2, LEN) = map(int, input().split())
	l1 -= 1
	l2 -= 1
	if zcount(l1, LEN) != zcount(l2, LEN):
		print('No')
		continue
	if zcount(l1, LEN) == 0:
		print('Yes')
		continue
	if first_check(l1, LEN) != first_check(l2, LEN):
		print('No')
		continue
	if zcount(l1, LEN) == 1:
		print('Yes')
		continue
	print(equalcheck(l1, l2, LEN))