1.Template.py

from __future__ import division, print_function
# import threading
# threading.stack_size(2**27)
# import sys
# sys.setrecursionlimit(10**7)
# sys.stdin = open('inpy.txt', 'r')
# sys.stdout = open('outpy.txt', 'w')
from sys import stdin, stdout
import bisect            #c++ upperbound
import math
import heapq
i_m=9223372036854775807
def inin():
    return int(input())
def stin():
    return input()
def spin():
    return map(int,stin().split())
def lin():                           #takes array as input
    return list(map(int,stin().split()))
def matrix(n):
    #matrix input
    return [list(map(int,input().split()))for i in range(n)]

################################################
def string2intlist(s):
    return list(map(int, s))

def calculate_sum(a, N): #sum of a to N
    # Number of multiples 
    m = N / a 
    # sum of first m natural numbers 
    sum = m * (m + 1) / 2
    # sum of multiples 
    ans = a * sum
    return ans
def series(N):
    return (N*(N+1))//2

def count2Dmatrix(i,list):
    return sum(c.count(i) for c in list)

def modinv(n,p):
    return pow(n, p - 2, p)
    
def nCr(n, r):
    i = 1
    while i < r:
        n *= (n - i)
        i += 1
    return n // math.factorial(r)

def GCD(x, y): 
    x=abs(x)
    y=abs(y)
    if(min(x,y)==0):
        return max(x,y)
    while(y): 
        x, y = y, x % y 
    return x
def LCM (x, y):
    return (x * y) // GCD(x, y)
    
def Divisors(n) : 
    l = []  
    for i in range(1, int(math.sqrt(n) + 1)) :
        if (n % i == 0) : 
            if (n // i == i) : 
                l.append(i) 
            else : 
                l.append(i)
                l.append(n//i)
    return l
def isprime(n):
    for i in range(2, int(math.sqrt(n))+1):
        if n%i==0:
            return False
    return True
prime=[]
def SieveOfEratosthenes(n): 
    global prime
    prime = [True for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * p, n+1, p): 
                prime[i] = False
        p += 1
    f=[]
    for p in range(2, n): 
        if prime[p]: 
            f.append(p)
    return f
q=[]       
def dfs(n,d,v,c):
    global q
    v[n]=1
    x=d[n]
    q.append(n)
    j=c
    for i in x:
        if i not in v:
            f=dfs(i,d,v,c+1)
            j=max(j,f)
            # print(f)
    return j
# d = {}
 
def knapSack(W, wt, val, n): 
    K = [[0 for x in range(W + 1)] for x in range(n + 1)] 
  
    # Build table K[][] in bottom up manner 
    for i in range(n + 1): 
        for w in range(W + 1): 
            if i == 0 or w == 0: 
                K[i][w] = 0
            elif wt[i-1] <= w: 
                K[i][w] = max(val[i-1] + K[i-1][w-wt[i-1]],  K[i-1][w]) 
            else: 
                K[i][w] = K[i-1][w] 
  
    return K[n][W]
"""*******************************************************"""