Oh, no!

The coronavirus has caught you, and now you're sitting in a dark cellar, with tied legs (but not hands). You have a delicious cookie, a laptop in front of you, and your ideal development environment is open. The coronavirus convinces you to solve the following problem.

You are given two arrays A and B of size n. You can do operations of two types with array A: 

  * Reverse array A. That is the array [A_1,\ A_2,\ …,\ A_n] transformes into [A_n,\ A_{n-1},\ …,\ A_1]. 
  * Replace A with an array of its prefix sums. That is, the array [A_1,\ A_2,\ …,\ A_n] goes to [A_1,\ (A_1+A_2),\ …,\ (A_1+A_2+…+A_n)]. 



You need to understand if you can get an array B from the array A. If it is possible, you will have to restore the order of these operations by minimizing the number of operations of the second type. Fortunately, the coronavirus is good today, so he has allowed you not to restore actions if the minimum number of second type operations is more than 2⋅ 10^5. But coronavirus resents you, so if you restore the answer, the total number of operations should not exceed 5⋅ 10^5.

Solve this problem and get the cookie, or the coronavirus will extend the quarantine for five years and make the whole economy collapse! 

Input

The first line contains a single integer n (1≤ n ≤ 2⋅ 10^5).

The second line contains n integers A_1, A_2, …, A_n (1 ≤ A_i ≤ 10 ^ {12}).

The third line contains n integers B_1, B_2, …, B_n (1 ≤ B_i ≤ 10 ^ {12}).

Output

If you cannot get B from the A array, print "IMPOSSIBLE" (without quotes) on a single line.

If the minimum number of operations of the second type exceeds 2⋅ 10^5, print "BIG" (without quotes). In the second line print the number of operations of the second type, that needs to be applied to get array B from A.

Otherwise, in the first line print "SMALL" (without quotes). In the second line print the total number of operations of the first and second types m ≤ 5⋅ 10^5 (it is guaranteed that in this case there is such a sequence of actions). In the third line print a line of length m, consisting of characters 'R"and 'P' (without quotes).

The i-th character should be 'R', if the i-th action is of the first type, and should be 'P', otherwise.

If there are several such sequences, you can print any of them.

You can print each character in the uppercase or in the lowercase.

Examples

Input


2
5 7
5 7


Output


SMALL
0



Input


2
1 1
300000 1


Output


BIG
299999


Input


2
10 1
13 14


Output


SMALL
6
RPPPRP


Input


3
1 2 1
2 1 2


Output


IMPOSSIBLE

Note

In the first example, the arrays A and B already equal, so the number of required operations =0.

In the second example, we need to replace A with the prefix sums 299999 times and then reverse the array. Since 299999>2⋅ 10^5, there is no need to restore the answer.

In the fourth example, you cannot get B from the A.

Difficulty: VERY_HARD
Tags: Sorting

Constructive algorithms

Implementation

Greedy algorithms
Skill types: Sorting

Greedy algorithms

Starter code:

Solutions:
import sys
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep='\n')

def II():
	return int(sys.stdin.readline())

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

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

def LLI(rows_number):
	return [LI() for _ in range(rows_number)]

def SI():
	return sys.stdin.readline()[:-1]

def main():
	n = II()
	aa = LI()
	raa = aa[::-1]
	bb = LI()
	if n == 1:
		if aa == bb:
			print('SMALL')
			print(0)
		else:
			print('IMPOSSIBLE')
		exit()
	if n == 2:
		mna = min(aa)
		cntp = 0
		(x, y) = bb
		if x > y:
			(x, y) = (y, x)
		while mna < x:
			c = y // x
			cntp += c
			y -= c * x
			if x > y:
				(x, y) = (y, x)
		d = y - max(aa)
		if mna != x or d % x:
			print('IMPOSSIBLE')
			exit()
		cntp += d // x
		if cntp > 200000:
			print('BIG')
			print(cntp)
			exit()
	ans = ''
	cntp = 0
	while 1:
		if aa == bb:
			if cntp > 200000:
				print('BIG')
				print(cntp)
			else:
				print('SMALL')
				print(len(ans))
				if ans:
					print(ans[::-1])
			exit()
		if raa == bb:
			if cntp > 200000:
				print('BIG')
				print(cntp)
			else:
				ans += 'R'
				print('SMALL')
				print(len(ans))
				if ans:
					print(ans[::-1])
			exit()
		if bb[0] <= bb[-1]:
			if cntp <= 200000:
				ans += 'P'
			cntp += 1
			for i in range(n - 2, -1, -1):
				bb[i + 1] -= bb[i]
				if bb[i + 1] <= 0:
					print('IMPOSSIBLE')
					exit()
		else:
			if cntp <= 200000:
				ans += 'R'
			bb.reverse()
main()


from bisect import *
from collections import *
from math import gcd, ceil, sqrt, floor, inf
from heapq import *
from itertools import *
from operator import add, mul, sub, xor, truediv, floordiv
from functools import *
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')

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())
from types import GeneratorType

def bootstrap(f, stack=[]):

	def wrappedfunc(*args, **kwargs):
		if stack:
			return f(*args, **kwargs)
		else:
			to = f(*args, **kwargs)
			while True:
				if type(to) is GeneratorType:
					stack.append(to)
					to = next(to)
				else:
					stack.pop()
					if not stack:
						break
					to = stack[-1].send(to)
			return to
	return wrappedfunc
farr = [1]
ifa = []

def fact(x, mod=0):
	if mod:
		while x >= len(farr):
			farr.append(farr[-1] * len(farr) % mod)
	else:
		while x >= len(farr):
			farr.append(farr[-1] * len(farr))
	return farr[x]

def ifact(x, mod):
	global ifa
	ifa.append(pow(farr[-1], mod - 2, mod))
	for i in range(x, 0, -1):
		ifa.append(ifa[-1] * i % mod)
	ifa = ifa[::-1]

def per(i, j, mod=0):
	if i < j:
		return 0
	if not mod:
		return fact(i) // fact(i - j)
	return farr[i] * ifa[i - j] % mod

def com(i, j, mod=0):
	if i < j:
		return 0
	if not mod:
		return per(i, j) // fact(j)
	return per(i, j, mod) * ifa[j] % mod

def catalan(n):
	return com(2 * n, n) // (n + 1)

def isprime(n):
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True

def lowbit(n):
	return n & -n

def inverse(a, m):
	a %= m
	if a <= 1:
		return a
	return (1 - inverse(m, a) * m) // a % m

class BIT:

	def __init__(self, arr):
		self.arr = arr
		self.n = len(arr) - 1

	def update(self, x, v):
		while x <= self.n:
			self.arr[x] += v
			x += x & -x

	def query(self, x):
		ans = 0
		while x:
			ans += self.arr[x]
			x &= x - 1
		return ans

class DSU:

	def __init__(self, n):
		self.c = [-1] * n

	def same(self, x, y):
		return self.find(x) == self.find(y)

	def find(self, x):
		if self.c[x] < 0:
			return x
		self.c[x] = self.find(self.c[x])
		return self.c[x]

	def union(self, u, v):
		(u, v) = (self.find(u), self.find(v))
		if u == v:
			return False
		if self.c[u] < self.c[v]:
			(u, v) = (v, u)
		self.c[u] += self.c[v]
		self.c[v] = u
		return True

	def size(self, x):
		return -self.c[self.find(x)]

class UFS:

	def __init__(self, n):
		self.parent = [i for i in range(n)]
		self.ranks = [0] * n

	def find(self, x):
		if x != self.parent[x]:
			self.parent[x] = self.find(self.parent[x])
		return self.parent[x]

	def union(self, u, v):
		(pu, pv) = (self.find(u), self.find(v))
		if pu == pv:
			return False
		if self.ranks[pu] >= self.ranks[pv]:
			self.parent[pv] = pu
			if self.ranks[pv] == self.ranks[pu]:
				self.ranks[pu] += 1
		else:
			self.parent[pu] = pv

def Prime(n):
	c = 0
	prime = []
	flag = [0] * (n + 1)
	for i in range(2, n + 1):
		if not flag[i]:
			prime.append(i)
			c += 1
		for j in range(c):
			if i * prime[j] > n:
				break
			flag[i * prime[j]] = prime[j]
			if i % prime[j] == 0:
				break
	return flag

def dij(s, graph):
	d = {}
	d[s] = 0
	heap = [(0, s)]
	seen = set()
	while heap:
		(dis, u) = heappop(heap)
		if u in seen:
			continue
		for v in graph[u]:
			if v not in d or d[v] > d[u] + graph[u][v]:
				d[v] = d[u] + graph[u][v]
				heappush(heap, (d[v], v))
	return d

def GP(it):
	return [[ch, len(list(g))] for (ch, g) in groupby(it)]

class DLN:

	def __init__(self, val):
		self.val = val
		self.pre = None
		self.next = None

def nb(i, j):
	for (ni, nj) in [[i + 1, j], [i - 1, j], [i, j - 1], [i, j + 1]]:
		if 0 <= ni < n and 0 <= nj < m:
			yield (ni, nj)

@bootstrap
def gdfs(r, p):
	if len(g[r]) == 1 and p != -1:
		yield None
	for ch in g[r]:
		if ch != p:
			yield gdfs(ch, r)
	yield None
t = 1
for i in range(t):
	n = N()
	a = RLL()
	b = RLL()
	if n == 1:
		if a == b:
			print('small')
			print('0')
			print()
		else:
			print('impossible')
	elif n == 2:
		if a == b:
			print('small')
			print('0')
			print()
		elif a == b[::-1]:
			print('small')
			print('1')
			print('r')
		else:
			(x, y) = (min(a), max(a))
			ans = ''
			(p, q) = (min(b), max(b))
			c = 0
			while p > x:
				c += q // p
				if c <= 2 * 10 ** 5:
					ans += 'p' * (q // p)
				(p, q) = (q % p, p)
				ans += 'r'
			if p < x:
				print('impossible')
			elif q < y or (q - y) % x:
				print('impossible')
			else:
				c += (q - y) // x
				if c > 2 * 10 ** 5:
					print('big')
					print(c)
				else:
					ans += 'p' * ((q - y) // x)
					print('small')
					res = ''
					if a == [y, x]:
						res += 'r'
					res += ans[::-1]
					if b[0] > b[1]:
						res += 'r'
					print(len(res))
					print(res)
	else:
		ans = []
		c = 0
		f = True
		ar = a[::-1]
		while b != a and b != ar:
			if b[1] < b[0]:
				b.reverse()
				ans.append('R')
			b = [b[i] - b[i - 1] if i else b[i] for i in range(n)]
			if min(b) <= 0:
				f = False
				break
			ans.append('P')
			c += 1
		if not f:
			print('impossible')
		elif c > 2 * 10 ** 5:
			print('big')
			print(c)
		else:
			if b == ar:
				ans.append('R')
			ans.reverse()
			print('small')
			print(len(ans))
			print(''.join(ans))


from sys import stdin, gettrace
if not gettrace():

	def input():
		return next(stdin)[:-1]

def main():
	n = int(input())
	aa = [int(a) for a in input().split()]
	bb = [int(a) for a in input().split()]
	if n == 1:
		if aa == bb:
			print('SMALL')
			print(0)
		else:
			print('IMPOSSIBLE')
	elif n == 2:
		pcount = 0
		res = []
		irev = False
		if aa[0] > aa[1]:
			aa.reverse()
			irev = True
		if bb[0] > bb[1]:
			bb.reverse()
			res.append('R')
		while bb[0] > aa[0]:
			pcount += bb[1] // bb[0]
			if pcount <= 200000:
				res += ['P'] * (bb[1] // bb[0]) + ['R']
			(bb[0], bb[1]) = (bb[1] % bb[0], bb[0])
		if bb[0] == aa[0] and (bb[1] - aa[1]) % bb[0] == 0:
			pcount += (bb[1] - aa[1]) // bb[0]
			if pcount <= 200000:
				res += ['P'] * ((bb[1] - aa[1]) // bb[0])
			if irev:
				res.append('R')
			if pcount > 200000:
				print('BIG')
				print(pcount)
			else:
				print('SMALL')
				print(len(res))
				print(''.join(res[::-1]))
		else:
			print('IMPOSSIBLE')
	else:
		res = []
		pcount = 0
		raa = list(reversed(aa))
		while bb != aa and bb != raa:
			if bb[1] < bb[0]:
				bb.reverse()
				res += ['R']
			bb = [bb[0]] + list(map(lambda x, y: y - x, bb[:-1], bb[1:]))
			if min(bb) <= 0:
				print('IMPOSSIBLE')
				return
			res += ['P']
			pcount += 1
		if pcount > 200000:
			print('BIG')
			print(pcount)
		else:
			print('SMALL')
			if bb != aa:
				res.append('R')
			print(len(res))
			print(''.join(res[::-1]))
main()


n = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
if n == 1:
	if A[0] == B[0]:
		print('SMALL')
		print(0)
		print()
	else:
		print('IMPOSSIBLE')
elif n == 2:
	out = []
	prefCount = 0
	works = True
	while B[0] + B[1] > A[0] + A[1] and B[0] and B[1]:
		if B[1] < B[0]:
			(B[0], B[1]) = (B[1], B[0])
			out.append(('R', 1))
		lim1 = B[1] // B[0]
		lim2 = (B[0] + B[1] - A[0] - A[1]) // B[0]
		do = min(lim1, lim2)
		if do == 0:
			do = 1
		B[1] -= do * B[0]
		out.append(('P', do))
		prefCount += do
	if A == B:
		pass
	elif A == B[::-1]:
		out.append(('R', 1))
	else:
		works = False
	if works:
		if prefCount > 2 * 10 ** 5:
			print('BIG')
			print(prefCount)
		else:
			print('SMALL')
			out = list(map(lambda x: x[0] * x[1], out))
			outS = ''.join(out[::-1])
			print(len(outS))
			print(outS)
	else:
		print('IMPOSSIBLE')
else:
	out = []
	prefCount = 0
	flipped = False
	works = True
	while B[0] + B[-1] > A[0] + A[-1] and works:
		if B[0] < B[-1]:
			for i in range(n - 1, 0, -1):
				if B[i] <= B[i - 1]:
					works = False
					break
				else:
					B[i] -= B[i - 1]
			if flipped:
				out.append('R')
				flipped = False
			out.append('P')
			prefCount += 1
		else:
			for i in range(n - 1):
				if B[i] <= B[i + 1]:
					works = False
					break
				else:
					B[i] -= B[i + 1]
			if not flipped:
				out.append('R')
				flipped = True
			out.append('P')
			prefCount += 1
	if flipped:
		B = B[::-1]
	if A == B:
		pass
	elif A == B[::-1]:
		out.append('R')
	else:
		works = False
	if works:
		if prefCount > 2 * 10 ** 5:
			print('BIG')
			print(prefCount)
		else:
			print('SMALL')
			print(len(out))
			print(''.join(out[::-1]))
	else:
		print('IMPOSSIBLE')


def is_asc(arr):
	a = arr[0]
	for b in arr[1:]:
		if a < b:
			a = b
		else:
			return False
	return True

def is_des(arr):
	a = arr[0]
	for b in arr[1:]:
		if a > b:
			a = b
		else:
			return False
	return True
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
result = []
count = 0
found = False
if N == 1:
	if A[0] == B[0]:
		found = True
elif N == 2:
	while True:
		if B[1] == 0:
			break
		if A[1] == B[1] and B[0] == A[0]:
			found = True
			break
		if A[0] == B[1] and B[0] == A[1]:
			result.append('R')
			found = True
			break
		if B[0] > B[1]:
			result.append('R')
			B.reverse()
		if B[0] < B[1]:
			if A[0] <= A[1]:
				if A[0] == B[0] and (B[1] - A[1]) % A[0] == 0:
					c = (B[1] - A[1]) // A[0]
					count += c
					if count <= 2 * 10 ** 5:
						result = result + ['P'] * c
					found = True
					break
			elif A[1] == B[0] and (B[1] - A[0]) % A[1] == 0:
				c = (B[1] - A[0]) // A[1]
				count += c
				if count <= 2 * 10 ** 5:
					result = result + ['P'] * c
					result.append('R')
				found = True
				break
			c = B[1] // B[0]
			count += c
			if count <= 2 * 10 ** 5:
				result = result + ['P'] * c
			B[1] = B[1] % B[0]
		else:
			break
else:
	while True:
		for (a, b) in zip(A, B):
			if a != b:
				eq = False
				break
		else:
			found = True
			break
		B.reverse()
		for (a, b) in zip(A, B):
			if a != b:
				eq = False
				break
		else:
			found = True
			result.append('R')
			break
		B.reverse()
		if is_des(B):
			B.reverse()
			result.append('R')
			count += 1
			result.append('P')
			for i in range(len(B) - 1, 0, -1):
				B[i] = B[i] - B[i - 1]
		elif is_asc(B):
			result.append('P')
			count += 1
			for i in range(len(B) - 1, 0, -1):
				B[i] = B[i] - B[i - 1]
		else:
			break
if found:
	if count <= 2 * 10 ** 5:
		print('SMALL')
		print(len(result))
		result.reverse()
		print(''.join(result))
	else:
		print('BIG')
		print(count)
else:
	print('IMPOSSIBLE')