"Night gathers, and now my watch begins. It shall not end until my death. I shall take no wife, hold no lands, father no children. I shall wear no crowns and win no glory. I shall live and die at my post. I am the sword in the darkness. I am the watcher on the walls. I am the shield that guards the realms of men. I pledge my life and honor to the Night's Watch, for this night and all the nights to come." — The Night's Watch oath.

With that begins the watch of Jon Snow. He is assigned the task to support the stewards.

This time he has n stewards with him whom he has to provide support. Each steward has his own strength. Jon Snow likes to support a steward only if there exists at least one steward who has strength strictly less than him and at least one steward who has strength strictly greater than him.

Can you find how many stewards will Jon support?

Input

First line consists of a single integer n (1 ≤ n ≤ 105) — the number of stewards with Jon Snow.

Second line consists of n space separated integers a1, a2, ..., an (0 ≤ ai ≤ 109) representing the values assigned to the stewards.

Output

Output a single integer representing the number of stewards which Jon will feed.

Examples

Input

2
1 5


Output

0

Input

3
1 2 5


Output

1

Note

In the first sample, Jon Snow cannot support steward with strength 1 because there is no steward with strength less than 1 and he cannot support steward with strength 5 because there is no steward with strength greater than 5.

In the second sample, Jon Snow can support steward with strength 2 because there are stewards with strength less than 2 and greater than 2.
#===============================================================================================
#importing some useful libraries.
from fractions import Fraction
import sys
import bisect
import heapq
from math import *
from collections import Counter as counter  # Counter(list)  return a dict with {key: count}
from itertools import combinations as comb # if a = [1,2,3] then print(list(comb(a,2))) -----> [(1, 2), (1, 3), (2, 3)]
from itertools import permutations as permutate
from bisect import bisect_left as bl
#If the element is already present in the list,
# the left most position where element has to be inserted is returned.
from bisect import bisect_right as br
from bisect import bisect
#If the element is already present in the list,
# the right most position where element has to be inserted is returned
 
#===============================================================================================
#some shortcuts
 
mod = 1000000007
def inp(): return sys.stdin.readline().strip() #for fast input
def out(var): sys.stdout.write(str(var))  #for fast output, always take string
def lis(): return list(map(int, inp().split()))
def stringlis(): return list(map(str, inp().split()))
def sep(): return map(int, inp().split())
def strsep(): return map(str, inp().split())
def graph(vertex): return [[] for i in range(0,vertex+1)]
def zerolist(n): return [0]*n
def nextline(): out("\n")  #as stdout.write always print sring.
def testcase(t):
    for p in range(t):
        solve()
def printlist(a) :
    for p in range(0,len(a)):
        out(str(a[p]) + ' ')
def lcm(a,b): return (a*b)//gcd(a,b)
def power(a,b):
    ans = 1
    while(b>0):
        if(b%2==1):
            ans*=a
        a*=a
        b//=2
    return ans

def createMatrix(rowCount, colCount, dataList):   
    mat = []
    for i in range (rowCount):
        rowList = []
        for j in range (colCount):
            if dataList[j] not in mat:
                rowList.append(dataList[j])
        mat.append(rowList)

    return mat
def isprime(n) : 
  
    if (n <= 1) :
        return False
    if (n <= 3) :
        return True
  
    
    if (n % 2 == 0 or n % 3 == 0) : 
        return False
  
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
  
    return True
    

import collections
"""def getFolderNames(names):
        exists = set()
        last = collections.defaultdict(int)
        result = []
        for name in names:
            k = last[name]
            modified = name
            while modified in exists:
                k += 1
                modified = f'{name}({k})'
            last[name] = k
            result.append(modified)
            exists.add(modified)
        return result

names = input()
#names = list(names)
print(getFolderNames(names))"""


"""n1, n2 = map(int, inp().split())
a = []
e = 0
g = 0
j = 0
k = []
#if(n1 == 2):
    #a.append(n1)
for i in range(n1, n2+1):
    if(isprime(i) == True):
        a.append(i)
#print(a)
#print(len(a))
b = []
s = ''
for i in range(len(a)):
    for j in range(len(a)):
        if(a[i] != a[j]):
            s = str(a[i])+str(a[j])
            b.append(int(s))
            s = ''
b = set(b)
b = list(b)
c = []
#print(b)
#print(len(b))
for i in range(len(b)):
    if(isprime(b[i]) == True):
        c.append(b[i])
#print(c)
#print(len(c))
c.sort()
e = c[0]
g = c[-1]
h = len(c)
print(e,g)
for i in range(2,h):
    j = e+g
    e = g
    g = j
    k.append(j)
#if(j > 10**15):
 #   j = j%mod
print(k)"""


"""for i in range(int(input())):
    n = int(input())
    a = 0
    while(n > 0):
        n = n//2
        a += 1
    print(a)"""

def minimalFilps1(bits): 
	n = len(bits) 

	# two arrays will keep the count for number 
	# of 0s' and 1s' to be flipped while 
	# traversing from left to right and right to 
	# left respectively 
	flipsFromLeft = [0 for i in range(n)] 
	flipsFromRight = [0 for i in range(n)] 

	# Fill flipsFromLeft[] 
	flips = 0
	for i in range(0, n, 1): 
		if (bits[i] == '1'): 
			flips = flips + 1	
		flipsFromLeft[i] = flips
	#print(flipsFromLeft)
	
	# Fill flipsFromRight[] 
	flips = 0
	i = n - 1
	while(i >= 0): 
		if (bits[i] == '0'): 
			flips = flips + 1
		i = i - 1
		flipsFromRight[i] = flips
	#print(flipsFromRight)
	
	# initialize minFlip to highest int value. 
	# If sum of leftflip and rightFlip is smaller 
	# than minflips, then update minFlips 
	minFlips1 = sys.maxsize 
	for i in range(1, n, 1): 
		if (flipsFromLeft[i - 1] +
			flipsFromRight[i] < minFlips1): 
			minFlips1 = (flipsFromLeft[i - 1] +
						flipsFromRight[i]) 
	
	return minFlips1 



def minimalFilps(bits): 
	n = len(bits) 

	# two arrays will keep the count for number 
	# of 0s' and 1s' to be flipped while 
	# traversing from left to right and right to 
	# left respectively 
	flipsFromLeft = [0 for i in range(n)] 
	flipsFromRight = [0 for i in range(n)] 

	# Fill flipsFromLeft[] 
	flips = 0
	for i in range(0, n, 1): 
		if (bits[i] == '0'): 
			flips = flips + 1	
		flipsFromLeft[i] = flips
	#print(flipsFromLeft)
	
	# Fill flipsFromRight[] 
	flips = 0
	i = n - 1
	while(i >= 0): 
		if (bits[i] == '1'): 
			flips = flips + 1
		i = i - 1
		flipsFromRight[i] = flips
	#print(flipsFromRight)
	
	# initialize minFlip to highest int value. 
	# If sum of leftflip and rightFlip is smaller 
	# than minflips, then update minFlips 
	minFlips = sys.maxsize 
	for i in range(1, n, 1): 
		if (flipsFromLeft[i - 1] +
			flipsFromRight[i] < minFlips): 
			minFlips = (flipsFromLeft[i - 1] +
						flipsFromRight[i]) 
	
	return minFlips 
def oddn(n):
    for i in range(2, n+1):
        if(i%2 != 0 and n%i == 0):
            return i
    return 3


"""n = int(input())
a = list(map(int, input().split()))
b = a.copy()
for i in range(n):
    if(a[i] == i+1):
        pass
    else:
        b[a[i]-1] = i+1
print(*b)"""


"""n = int(input())
a = list(map(int, input().split()))
b = a.copy()
minb = 0
maxb = 0
mnxb = []
for i in range(n-1):
    if(a[i]<0 and i == 0):
        minb = abs(a[i]-a[i+1])
        maxb = abs(a[i]-a[n-1])
        mnxb.append((minb,maxb))
    elif(a[i]<0 and i>0):
        minb = min(abs(a[i]-a[i-1]),abs(a[i]-a[i+1]))
        maxb = max(abs(a[i]-a[n-1]),abs(a[i]-a[0]))
        mnxb.append((minb,maxb))
    elif(a[i]>0 and i == 0):
        minb = abs(a[i]-a[i+1])
        maxb = abs(a[i]-a[n-1])
        mnxb.append((minb,maxb))
    else:
        minb = min(abs(a[i]-a[i-1]),abs(a[i]-a[i+1]))
        maxb = max(abs(a[i]-a[n-1]),abs(a[i]-a[0]))
        mnxb.append((minb,maxb))
mnxb.append((abs(a[n-1]-a[n-2]),abs(a[n-1]-a[0])))
for i in range(n):
    print(*mnxb[i])"""


"""a = input()
b = input()
a = list(a)
b = list(b)
c = max(len(a), len(b))
d = 0
if(a == b):
    d = -1
    print(d)
else:
    if(len(a) > len(b)):
        print(len(a))
    elif(len(a) < len(b)):
        print(len(b))
    else:
        print(c)"""


"""n = int(inp())
a = list(map(int, inp().split()))
b = a.copy()
c = []
for i in range(n):
    if(a[i] == max(b)):
        c.append(a[i])
        c.sort(reverse = True)
        print(*c)
        for i in range(len(c)):
            b.remove(c[i])
        c.clear()
    else:
        print()
        c.append(a[i])"""


n = int(input())
a = list(map(int, input().split()))
b = 0
if(n == 1 or n == 2):
    b = 0
else:
    c = min(a)
    d = max(a)
    for i in range(n):
        if(a[i] > c and a[i] < d):
            b += 1
print(b)


        
    
        
    
        
        

        
        
    
"""n = int(input())
a = list(map(int, input().split()))
b = [0]*n
c = [0]*n
b[0] = 1
for i in range(1, n):
    if(a[i] >= a[i-1]):
        b[i] = b[i-1] + 1
    else:
        b[i] = 1
c[n-1] = 1
for i in range(n-2,-1,-1):
    if(a[i] >= a[i-1]):
        c[i] = c[i+1]+1
    else:
        c[i] = 1
mx = 0
for i in range(n):
    mx = max(mx, b[i]+c[i]-1)
print(mx)"""

    


    
"""for i in range(int(inp())):
    n = int(inp())
    a = 0
    if(n == 1):
        a = 0
    while(n > 1):
        if(n%oddn(n) == 0):
            #print(oddn(n))
            n = n//(oddn(n))
            a += 1
        else:
            n = n-1
            a += 1
    if(a == 0):
        print("FastestFinger")
    elif(a%2 != 0):
        print("Ashishgup")
    else:
        print("FastestFinger")"""


"""for i in range(int(inp())):
    n = int(inp())
    a = list(map(int, inp().split()))
    e_i = []
    o_i = []
    for i in range(len(a)):
        if(a[i]%2 == 0):
            e_i.append(i+1)
            
        else:
            o_i.append(i+1)
    index_list = []
    if(len(e_i)%2 == 0 and len(o_i)%2 == 0):"""


"""n, start = map(int, inp().split())
nums = []
for i in range(n):
    nums.append(start + 2*i)
xor_nums = 0
for i in range(n):
    xor_nums = xor_nums^nums[i]
print(xor_nums)"""


    
"""for i in range(int(inp())):
    n = int(inp())
    a = 0
    #while(n >= 1):
    if(n%2 == 0):
        a = n//2
    else:
        #a.append(gcd(n-1,(n-1)//2))
        a = (n-1)//2
        #if(n%3 == 0):
            #a.append(gcd(n,n//3))
        #if(n%5 == 0):
            #a.append(gcd(n,n//5))
        #if(n%7 == 0):
            #a.append(gcd(n,n//7))
        #n -= 1
    print(a)"""
    
            

"""for i in range(int(input())):
    s = input()
    a = 0
    b = 0
    for i in range(len(s)):
        if(s[i] == '0'):
            a += 1
        else:
            b += 1
    pre_0 = [0]*len(s)
    pre_1 = [0]*len(s)
    if(s[0] == '0'):
        pre_0[0] = 1
        pre_1[0] = 0
    else:
        pre_0[0] = 0
        pre_1[0] = 1
    #print(pre_0[0])
    #print(pre_1[0])
    for i in range(1,len(s)):
        if(s[i] == '0'):
            pre_0[i] = pre_0[i-1]+1
            pre_1[i] = pre_1[i-1]
        else:
            pre_0[i] = pre_0[i-1]
            pre_1[i] = pre_1[i-1]+1
    #print(pre_0)
    #print(pre_1)
    e = sys.maxsize
    for i in range(len(s)):
        e = min(e, pre_0[i]+(b-pre_1[i]))
        e = min(e, pre_1[i]+(a-pre_0[i]))
    print(e)"""
    
    
              


"""for i in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))
    c = []
    for i in range(n):
        c.append([a[i],b[i]])
    #print(c)
    c = sorted(c,key=lambda c:c[1])
    #print(c)
    d = []
    e = []
    for i in range(len(c)):
        d.append(c[i][0])
        e.append(c[i][1])
    #print(d)
    #print(e)
    g = []
    i = 0
    g.append(
    for j in range(1,n):
        if(d[j] >= e[i]):
            g.append(j+1)
            i = j
    print(*g)"""


"""for i in range(int(input())):
    a, b, n = map(int, input().split())
    d = []
    c = b
    e = []
    g = a
    h = b
    for i in range(n):
        b = a
        a += c
        c = b
        d.append(a)
        if(a > n):
            break
    for i in range(n):
        a = h
        h += g
        g = a
        e.append(h)
        if(h > n):
            break
        
    #print(d)
    #print(len(d))
    #print(e)
    print(min(len(e), len(d)))"""
    
    
    
    
    
        
    
    

    
        
    

"""for i in range(int(input())):
    n, s, k = map(int, input().split())
    a = list(map(int, input().split()))
    l = 1
    r = n
    b = 0
    c = n
    while(l <= r):
        m = (l+r)//2
        if m not in a and (abs(s-m)<=m//2+s):
            b = m
            #c = abs(s-m)
            r = m-1
        else:
            l = m+1
    print(abs(s-b))"""
    

"""for i in range(int(inp())):
    s = inp()
    a = list(s)
    b = []
    for i in range(len(a)):
        c = int(a[i])*(10**(len(a)-i-1))
        #print(c)
        if(c > 0):
            b.append(c)
    print(len(b))
    print(*b)"""
    
    
    
    
    
    


"""for i in range(int(inp())):
    a1, b1 = list(map(int, inp().split()))
    a2, b2 = list(map(int, inp().split()))
    a = min(a1, b1)
    b = min(a2, b2)
    c = a+b
    d = max(a1, b1)
    e = max(a2, b2)
    if(d != e):
        print("NO")
    else:
        if(c == d and c == e):
            print("YES")
        else:
            print("NO")"""
            
    


"""s = inp()
a = list(s)
b = {}
c = ''
for i in a:
    if i in b:
        b[i] += 1
    else:
        b[i] = 1
for key,val in b.items():
    if(val == 1):
        c = key
        break
#print(b)
print(c)"""


"""s = inp()
b = counter(s)
a = ''
print(str(b))
for key,val in b.items():
    if(val == 1):
        a = key
        break
if(a == ''):
    print(s[0])
else:
    print(a)"""
    




"""for i in range(int(inp())):
    n, k = map(int, inp().split())
    s = inp()
    a = list(s)
    b = []
    c = []
    d = []
    g = []
    e = 0
    h = 0
    l = 0
    for i in range(n):
        if(a[i] == '1'):
            b.append(i)
    #print(b)
    if(len(b) == 0):
        if(n%2 == 0):
            e = n//(k+1)
        else:
            e = 1 + n//(k+1)
    elif(len(b) == 1):
        d = a[:len(b)+1]
        g = a[len(b):]
        #print(d)
        #print(g)
        for i in range(len(d)):
            if(d[i] == '0'):
                h += 1
        for i in range(len(g)):
            if(g[i] == '0'):
                l += 1
        if(h>0 and l>0 and (h//(k+1) >= k or l//(k+1) >= k)):
            e = h//(k+1) + l//(k+1)
        elif(l>0 and l//((k+1)>=k)):
             e = l//(k+1)
        else:
             e = h//(k+1)
        
                
        #else:
            #if(n//(k+1) >= k):
                #e = n//(k+1)
        
    else:
        for i in range(len(b)-1):
            c = a[b[i]:b[i+1]+1]
            #print(c)
            d = len(c)-2
            if(k == 1):
                e += (d-1)//(k+1)
            else:
                if((d-1)//(k+1) >= k):
                    e += d//(k+1)
    print(e)"""
    
                


"""for i in range(int(inp())):
    a = inp()
    b = list(a)
    c = []
    c.append(b[0])
    #c = b.copy()
    for i in range(1,len(b), 2):
            c.append(b[i])
            #print(c)
        #if(c[-1] != b[-1]):
    #c.append(b[-1])
    c = ''.join(map(str, c))
    out(c)
    nextline()"""
    
    

"""for i in range(int(inp())):
    n = int(inp())
    a = list(map(int, inp().split()))
    o = 0
    e = 0
    b = 0
    if(n%2 == 0):
        for i in range(n):
            if(a[i]%2 == 0):
                e += 1
            else:
                o += 1
        #print(e,o)
        if(e == o):
            for i in range(n):
                if((a[i]%2 == 0 and i%2 == 0)or (a[i]%2 != 0 and i%2 != 0)):
                   pass
                else:
                   b += 1
        else:
            b = -1
    else:
        for i in range(n):
            if(a[i]%2 == 0):
                e += 1
            else:
                o += 1
        #print(e,o)
        if(e%2 != o%2 and e-o==1):
            if(n > 1 and e>=1 and o>=1):
                for i in range(n):
                    if((a[i]%2 == 0 and i%2 == 0)or (a[i]%2 != 0 and i%2 != 0)):
                       pass
                    else:
                       b += 1
            elif(n == 1 and e == 1):
                b = 0
            else:
                b = -1
        else:
            b = -1
    if(b<0):
        print(b)
    else:
        print(b//2)"""
        
            
            
            
            


"""for i in range(int(input())):
    n, k = map(int, input().split())
    a = floor((k-1)/(n-1))+k
    print(a)"""

"""for i in range(int(input())):
    n, k = map(int, input().split())
    l = 1
    r = 2*k
    a = 0
    while( l <= r):
        m = (l+r)//2
        if(m-m//n >= k):
            a = m
            r = m-1
        else:
            l = m+1
    print(a)"""
    
    

"""n, m = list(map(int, input().split()))
xc, yc = list(map(int, input().split()))
k = int(input())
a = 0
for i in range(k):
    dx, dy = map(int, input().split())
    #c.append([dx,dy])
    #c.append(dy)
    #d.append(c)
    #c.pop()
    #c.pop()
    l = 0
    r = 10**9
    b = 0
    while(l <= r):
        mid = (l+r)//2
        if(1 <= xc+dx*mid <= n and 1<= yc+dy*mid <= m):
            b = mid
            l = mid+1
        else:
            r = mid-1
    xc = xc+dx*b
    yc = yc+dy*b
    a += b
print(a)"""

    

    


"""n, a = map(int, input().split())
b = list(map(int, str(n)))
for i in range(a):
    if(b[-1] == 0):
        b.pop()
    else:
        b[-1] = b[-1] - 1
print(''.join(map(str,b)))"""

"""n = int(input())
s = input()
a = list(s)
b = 0
for i in range(n-1):
    if(a[i] == a[i+1]):
        b += 1
print(b)"""

"""s = input()
a = list(s)
b = 1
c = 1
d = 0
e = 0
h = 0
m = 1000000007
if 'c' in a or 'k' in a:
    d = 0
else:
    for i in range(len(a)-1):
        if(a[i] == 'g' and a[i+1] == 'g'):
            b += 1
        if(a[i] == 'f' and a[i+1] == 'f'):
            c += 1
    if(b == 1 and c == 1):
        for i in range(len(a)):
            if(a[i] == 'g'):
                e += 1
            if(a[i] == 'f'):
                h += 1
        if(e == 1 and h == 1):
            d = 1
        else:
            d = e%m + h%m
    elif(b == 1):
        b = 0
        d = b%m + c%m
    elif(c == 1):
        c = 0
        d = b%m + c%m
    else:
        d = b%m * c%m
print(d)
#print(b,c)"""



"""n, k = map(int, input().split())
l = 0
r = n-1
c = 0
while(l <= r):
    m = (l+r)//2
    a = m*(m+1)//2
    b = n-m
    if(a-b == k):
        c = b
        break
    elif(a-b > k):
        r = m-1
    else:
        l = m+1
        #b = a - k
        #print(b,b+m)
        #print(m)
        #if(b+m == n):
            #break
print(c)"""



"""for i in range(int(input())):
    n = int(input())
    a = []
    b = []
    c = n//2
    if(c%2 != 0):
        print("NO")
    else:
        for i in range(1,n+1):
            if(i%2 == 0):
                a.append(i)
        #print(a)
        for i in range(1,a[len(a)-2]):
            if(i%2 != 0):
                b.append(i)
        d = sum(a)-sum(b)
        #print(b)
        if(d%2 != 0):
            b.append(d)
            print("YES")
            print(*(a+b))
        else:
            print("NO")"""
        
            
        


"""for i in range(int(input())):
    n = int(input())
    a = n//2
    s = 8*((a*(a+1)*(2*a+1))//6)
    print(s)"""
    


"""for i in range(int(input())):
    n, s, k = map(int, input().split())
    a = list(map(int, input().split()))
    a = set(a)
    d = 10^5
    e = 10^5
    if s in a:
        b = [x for x in range(1,s)]
        c = [x for x in range(s+1,n+1)]
        c.sort(reverse = True)
        #print(b)
        #print(c)
        if(len(b) == 0):
            for i in range(k):
                if min(c) in a:
                    c.pop()
                    if(len(c) == 0):
                        break
                else:
                    e = min(c)-s
                    break
        elif(len(c) == 0):
            for i in range(k):
                if max(b) in a:
                    b.pop()
                    if(len(b) == 0):
                        break
                else:
                    d = s-max(b)
                    break
        else:
            for i in range(k):
                if max(b) in a:
                    b.pop()
                    if(len(b) == 0):
                        break
                else:
                    d = s-max(b)
                    break
            for i in range(k):
                if min(c) in a:
                    c.pop()
                    if(len(c) == 0):
                        break
                else:
                    e = min(c)-s
                    break
        print(min(d,e))
    else:
        print(0)"""
    
    


"""n = int(input())
m = int(input())
a = []
for i in range(n):
    a.append(int(input()))
kmax = max(a)+m
a.sort()
for i in range(m):
    a[0] = a[0] + 1
    a.sort()
#print(a)
print(max(a), kmax)"""




"""for i in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    b = set(a)
    c = 1
    d = []
    a.sort()
    if(len(a) == 1):
        e = 0
    else:
        if(a == list(b)):
            e = 1
        else:
            #for i in range(n):
                #d[a[i]] += 1
            #for i in range(len(d)):
                #if(d[i] > 1 and d[i]%2 == 0):
                    #c += 1
            #print(d)
            for i in range(n-1):
                if(a[i] == a[i+1]):
                    c += 1
                elif(c == 1):
                    pass
                else:
                    d.append(c)
                    c = 1
            if(c>1):
                d.append(c)
            #print(d)
            #if(max(d) == 1):
                #e = 2
            #elif(max(d) == 2):
                #e = max(d)+1
            #else:
            e = max(min(len(b)-1,max(d)),min(len(b),max(d)-1))
    print(e)"""
    
        


"""n, k = map(int, input().split())
l = []
d = 0
for i in range(n):
    a,b = map(int, input().split())
    l.append((a,-b))
#a = sorted(a,key=lambda a: (a[0],a[1]))
l.sort(reverse = True)
#print(l)
c = l[k-1]
#print(c)
for i in range(n):
    if(l[i] == c):
        d += 1
print(d)"""




"""n, k = map(int, input().split())
a = 240
b = a-k
c = 0
d = []
for i in range(1,n+1):
    c += 5*i
    if(b-c >= 0):
        #print(b-c)
        d.append(i)
#print(d)
if(len(d) == 0):
    d.append(0)
print(max(d))"""




"""for i in range(int(input())):
    n = int(input())
    for i in range(2,30):
        b = 2**i - 1
        if(n%b == 0):
            d = n//b
    print(d)"""



"""for i in range(int(input())):
    n, x, m = map(int, input().split())
    a = x
    b = x
    for i in range(m):
        l, r = map(int, input().split())
        if(l <= a <= r):
            a = l
        if(l <= b <= r):
            b = r
    print(b-a+1)"""
    
                
                


"""for i in range(int(input())):
    a, b = map(int, input().split())
    if(a == 0 or b == 0):
        c = 0
    else:
        c = a+b
    d = min(c//3, min(a,b))
    print(d)"""



"""n = int(input())
a = list(map(int, input().split()))
b = 1
e = []
for i in range(n-1):
    if(a[i] == a[i+1]):
        b += 1
    else:
        e.append(b)
        b = 1
e.append(b)
print(e)
h = 0
for i in range(len(e)-1):
    h = max(h,min(e[i],e[i+1]))
print(2*h)"""



"""a, b, c = map(int, input().split())
#e = max(a,b,c)
for i in range(1,a*c):
    if(a*c - i*b <= b*c):
        d = i
        break
print(d)"""



"""for i in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    a.sort()
    b = []
    #b = a[-1] - a[0]
    for i in range(n):
        for j in range(i+1, n):
            b.append(a[j]-a[i])
    print(min(b))"""
     


"""for i in range(int(input())):
    a, b = map(int, input().split())
    if(a<b):
        a, b = b, a
    c = 4*b**2
    if(2*b < a):
        c = a**2
    print(c)"""

    
    


"""n=int(input())
l=[int(i) for i in input().split()]
s=list(input())
sm=0 
for i in range(n):
    if s[i]=='B': 
        sm+=l[i]
        l[i]=-l[i]
print(l)
maxi1=0 
sm1=0 
for i in range(n):
    sm1+=l[i]
    maxi1=max(maxi1,sm1)
sm2=0 
maxi2=0 
for i in range(n-1,-1,-1):
    sm2+=l[i]
    maxi2=max(maxi2,sm2)
print(sm2)
print(maxi1,maxi2)
print(sm+max(maxi1,maxi2))"""


"""n = int(input())
a = list(map(int, input().split()))
b = input()
b = list(b)
d = 0
h = []
l = []
if(n == 1):
    h.append(a[0])
else:
    for i in range(n):
        if(b[i] == 'A'):
            d += 1
    if(d == n):
        h.append(sum(e))
    else:
        for i in range(n-1, -1, -1):
            if(b[i] == 'B'):
                h.append(a[i])
            elif(b[i] == 'A'):
                l.append(a[i])
                #h.append(i+1)
                #break
            else:
                pass
        h.append(max(l))
print(sum(h))"""


        


        
    


"""for i in range(int(input())):
    n, m = map(int, input().split())
    a = list(map(int, input().split()))
    b = sum(a)
    if(m <= b):
        print(m)
    else:
        print(b)"""
    



"""n = int(input())
a = input()
a = list(a)
b = []
d = 0
e = 1
if(len(a) == 1):
    if(a[0] == '0'):
        e = 0
else:
    for i in range(n):
        if(a[i] == '1'):
            b.append(i)
    if((a[0] == '0' and a[1] == '0') or (a[-1] == '0' and a[-2] == '0')):
        e = 0
    else:
        for i in range(len(b)-1):
            for j in range(b[i], b[i+1]+1):
                #print(j)
                #print(a[j])
                if(a[j] == '0'):
                    d += 1
            #print(d)
            if(d > 2 or d == 0):
                e = 0
                break
            d = 0
if(e == 1):
    print("Yes")
else:
    print("No")

            
#print(b)"""


"""n = int(input())
a = list(map(int, input().split()))
b = 0
d = 0
e = 0
o = 0
g = []
h = []
m = []
for i in range(n):
    if(a[i]<0):
        b += 1
    elif(a[i]>0):
        d += 1
    else:
        e += 1
for i in range(n):
    if(b%2 == 1):
        if(a[i] < 0 and len(g) == 0):
            g.append(a[i])
        elif(a[i] > 0 or a[i] < 0):
            h.append(a[i])
        else:
            m.append(a[i])
    elif(b%2 == 0):
        if(a[i]<0 and len(g) == 0):
            g.append(a[i])
        elif(a[i]<0):
            if(d == 0):
                h.append(a[i])
            else:
                m.append(a[i])
        elif(a[i]>0):
            h.append(a[i])
        else:
            m.append(a[i])
    #if(a[i] == 0):
        #m.append(a[i])
if(d == 0 and len(h)%2 != 0):
    o = h.pop()
    m.append(o)
print(len(g),*g)
print(len(h),*h)
print(len(m),*m)"""
    


"""n, m, k = map(int, input().split())
a = []
b = []
d = 0
e = 0
for i in range(m+1):
    x = int(input())
    a.append(x)
for i in range(m):
    b.append(bin(a[-1]^a[i]).replace("0b",""))
#print(b)
for i in b:
    c = list(i)
    #print(c)
    for j in range(len(c)):
        if(c[j] == '1'):
            d += 1
    #print(d)
    if(d <= k):
        e += 1
    d = 0
        
print(e)
#print(a)"""



"""a, b = map(int, input().split())
c = a+b
d = 0
e = 0
if(a == 0 and b == 0):
    print("NO")
else:
    if(c%2 == 0):
        d = c//2
        e = c//2
    else:
        d = c//2
        e = c//2+1
    if(a == d or a == e and b == e or b == d):
        print("YES")
    else:
        print("NO")"""
    


"""n, m = map(int, input().split())
a = []
b = []
d = []
e = 0
for i in range(n):
    s = input()
    s = list(s)
    a.append(s)
for i in range(len(a)):
    for j in range(i+1, len(a)):
        if(a[i] == a[j][::-1]):
            if(len(b) == 0):
                b.insert(0,''.join(map(str,a[i])))
                b.insert(1,''.join(map(str,a[j])))
            else:
                b.insert(0,''.join(map(str,a[i])))
                b.insert(len(b),''.join(map(str,a[j])))
    #print(b)
    if(len(a[i])%2 == 0):
        if(a[i][:len(a[i])//2] == a[i][len(a[i])//2:][::-1]):
            e = 1
            if(len(d) == 0):
                b.insert(len(b)//2,''.join(map(str,a[i])))
                d.append(''.join(map(str,a[i])))
                #break
            #else:
                #b.insert(0,''.join(map(str,a[i])))
                #d.append(''.join(map(str,a[i])))
    else:
        if(a[i][:len(a[i])//2+1] == a[i][len(a[i])//2:][::-1]):
            e = 1
            if(len(d) == 0):
                b.insert(len(b)//2,''.join(map(str,a[i])))
                d.append(''.join(map(str,a[i])))
                #break
            #else:
                #b.insert(0,''.join(map(str,a[i])))
                #d.append(''.join(map(str,a[i])))
                
print(len(''.join(map(str,b))))
print(''.join(map(str,b)))
#print(d)
#print(e)
#print(a)"""




"""s = input()
s = list(s)
a = []
b = []
d = 0
if(len(s)%2 == 0):
    a.append(s[:len(s)//2])
    b.append(s[len(s)//2:])
else:
    a.append(s[:len(s)//2+1])
    b.append(s[len(s)//2:])
#b = b[::-1]
a = sum(a,[])
b = sum(b,[])
#print(a)
#print(b)
for i in range(len(a)):
    if(a[i] != b[len(a)-i-1]):
        d += 1
        #print(a[i])
        #print(b[len(a)-1-i])
    #else:
        #print(a[i])
        #print(b[len(a)-i-1])
#print(d)
if(d == 1 and len(s)%2 == 0):
    print("YES")
elif(d == 0 and len(s)%2 == 0):
    print("NO")
elif((d == 0 or d == 1) and len(s)%2!=0):
    print("YES")
else:
    print("NO")"""


    
    
    


"""n, k = map(int, input().split())
a = list(map(int, input().split()))
i = 1
while(k-i > 0):
    k -= i
    i += 1

#b = []
#for i in range(1,n+1):
    #b.append(a[0:i])
#b = sum(b,[])
#print(b)
print(a[k-1])"""



"""n = int(input())
a = 0
b = 0
d = n%7
if(d == 0):
    e = n//7
    a = 2*e
    b = 2*e
else:
    if(n<7):
        if(d == 1):
            a = 0
            b = 1
        elif(d > 1 and d < 6):
            a = 0
            b = 2
        else:
            a = 1
            b = 2
    else:
        e = n//7
        a = 2*e
        b = 2*e
        if(d == 1):
            b += 1
        elif(d<6):
            b += 2
        else:
            a += 1
            b += 2
print(a, b)""" 


"""for i in range(int(input())):
    n, m = list(map(int, input().split()))
    a = [[int(x) for x in input().split()] for _ in range(n)]
    r = set()
    c = set()
    #print(a)
    for i in range(n):
        for j in range(m):
            if(a[i][j] == 1):
                r.add(i)
                c.add(j)
    b = min(n-len(r), m-len(c))
    
    if(b%2 == 0):
        print("Vivek")
    else:
        print("Ashish")"""


"""for i in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))
    d = 0
    e = 0
    g = 0
    c = sorted(a)
    if(a == c):
        d = 1
    else:
        for i in range(n):
            if(b[i] == 0):
                e += 1
            else:
                g += 1
    if(e and g):
        d = 1
    if(d == 1):
        print("Yes")
    else:
        print("No")"""
    
    
    
    
"""def createMatrix(rowCount, colCount, dataList):   
    mat = []
    for i in range (rowCount):
        rowList = []
        for j in range (colCount):
            if dataList[j] not in mat:
                rowList.append(dataList[j])
        mat.append(rowList)

    return mat 

    
for i in range(int(input())):
    n = int(input())
    r = n
    c = n
    a = [x for x in range(1,n**2+1)]
    m = createMatrix(r,c,a)
    if(n == 2):
        for i in range(n):
            for j in range(n-1):
                if(i%2 != 0):
                    m[i][j], m[i][n-1-j] = m[i][n-1-j], m[i][j]
    else:
        for i in range(n):
            for j in range(n-2):
                if(i%2 != 0):
                    m[i][j], m[i][n-1-j] = m[i][n-1-j], m[i][j]
                #if((m[i][j] + m[n-1-i][n-1-j])%2 != 0):
                    #m[n-1-i][n-1-j], m[n-1-i][n-1-j-1] = m[n-1-i][n-1-j-1], m[n-1-i][n-1-j]
                #else:
                    #m[n-1-i][n-1-j], m[n-1-i][n-1-j-1] = m[n-1-i][n-1-j-1], m[n-1-i][n-1-j]
    for i in range(n):
        for j in range(n):
            print(m[i][j], end=' ')
        print( )"""
    
    
    
    
            
    
    
        


"""for i in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    b = 0
    c = 0
    d = 1
    e = 0
    if(len(a) == 1):
        if(a[0] == 5):
            d = 1
        else:
            d = 0
    else:
        #b.append(a[0])
        for i in range(1, n):
            if(a[i] == 10):
                c += 1
                if(b > 0):
                    b = b-1
                else:
                    d = 0
                    break
                #if(a[i] - b <= 5):
                    #b.append(a[i] - sum(b))
                    #b += a[i]-5
            elif(a[i] == 15):
                e += 1
                if(c > 0):
                    c = c-1
                elif(b > 1):
                    b = b-2
                else:
                    d = 0
                    break
            else:
                #b = b + a[i]
                b += 1
                    
        
    #if(e == 0):
        #if(c <= b and c>=1 and b>=1):
            #d = 1
        #else:
            #d = 0
    #else:
        #if(e<=c and c<=b and c>=1 and b>=1):
            #d = 1
        #else:
            #d = 0
    if(d == 1):
        print("YES")
    else:
        print("NO")"""
    
    
    


"""for i in range(int(input())):
    s = input()
    a = 0
    s = list(s)
    j = 1
    for i in range(0, len(s)-1):
    #while(len(s) != 0):
        if(len(s) == 0):
            break
        if((s[i] =='x' and s[i+1] == 'y') or (s[i] == 'y' and s[i+1] == 'x')):
            a += 1
            s[i+1] = 'z'
            #print('a')
            #print(j)
        #else:
            #j -= 1
            #print(j)
            #s.remove(i)
            #s.remove(i+1)
            #if(len(s) == 0):
                #break
    print(a)"""
    
    

"""for i in range(int(input())):
    n, k = map(int, input().split())
    p = list(map(int, input().split()))
    a = 0
    for i in range(n):
        if(p[i] > k):
            a += p[i] - k
    print(a)"""


"""for i in range(int(input())):
    ts = int(input())
    a = 0
    b = 0
    if(ts == 1):
        b = 0
    else:
        if(ts%2 != 0):
            a = ts//2+1
            b = ts-a
        else:
            d = 0
            while(ts%2 == 0):
                d += 1
                ts = ts//2
            if(ts%2 != 0):
                a = ts//2+1
                b = ts-a
    print(b)"""
    

"""for i in range(int(input())):
    n = int(input())
    s = list(map(int, input().split()))
    a = []
    c = []
    s.sort()
    for k in range(1,1024):
        for i in s:
            b = i^k
            a.append(b)
        #print(a)
        #print(s)
        if(s == sorted(a)):
            c.append(k)
        a.clear()
    if(len(c) == 0):
        c.append(-1)
    print(min(c))"""
    
            


"""for i in range(int(input())):
    a, b = map(int, input().split())
    c = 0
    if(a == b):
        c = 0
    elif(a > b):
        d = a/b
        if(d == a//b):
            if(d == 1 and a == b):
                c = 0
            elif(d == 2 or d == 4 or d == 8):
                c = 1
            elif(d > 8 and d%2 == 0):
                while(d != 1):
                    if(d%8 == 0):
                        d = d//8
                        c += 1
                    elif(d%4 == 0):
                        d = d//4
                        c += 1
                    elif(d%2 == 0):
                        d = d//2
                        c += 1
                    else:
                        c = -1
                        break
            else:
                c = -1
        else:
            c = -1
    else:
        d = b/a
        if(d == b//a):
            if(d == 1 and b == a):
                c = 0
            elif(d == 2 or d == 4 or d == 8):
                c = 1
            elif(d > 8 and d%2 == 0):
                while(d != 1):
                    if(d%8 == 0):
                        d = d//8
                        c += 1
                    elif(d%4 == 0):
                        d = d//4
                        c += 1
                    elif(d%2 == 0):
                        d = d//2
                        c += 1
                    else:
                        c = -1
                        break
            else:
                c = -1
        else:
            c = -1
    print(c)"""
    
        
        


"""for i in range(int(input())):
    s = input()
    a = list(s)
    d = ['0', '1', '0']
    e = ['1', '0', '1']
    b = 0
    if(len(a) < 3):
        b = 0
    elif(len(a) == 3):
        if(a != d and a != e):
            b = 0
        else:
            b = 1
    else:
        g = 0
        h = 0
        for i in a:
            if(i == '0'):
                g += 1
            else:
                h += 1
        if(g <= 1 or h <= 1):
            b = 0
        if(g < h):
            b = g
        else:
            b = h
    print(b)"""
    
        


"""for i in range(int(input())):
    n, x = map(int, input().split())
    a = list(map(int, input().split()))
    b = 0
    c = 0
    d = 0
    if(len(a) == 1):
        if(a[0]%2 == 0):
            b = 0
        else:
            b = 1
    else:
        for i in a:
            if(i%2 == 0):
                c += 1
            else:
                d += 1
        if(x < c+d):
            if(c and d > 1):
                b = 1
            elif(c == 0 and x%2 == 0):
                b = 0
            elif(d == 0):
                b = 0
            else:
                b = 1
        else:
            #if(x%2 == 0):
            if(d%2 != 0):
                b = 1
            else:
                b = 0
    if(b == 0):
        print("No")
    else:
        print("Yes")"""
    #print(b)
    
            


#import math
"""for i in range(int(input())):
    n, m, k = map(int, input().split())
    c = n//k
    if(m == 0):
        d = 0
    elif(m <= c):
        d = m
    else:
        d = (m-c)//(k-1)
        if((m-c)%(k-1) != 0):
            d += 1
        d = c - d
            #d = c - math.ceil((m-c)/(k-1))
        #else:
            #d = c - 1
        #if(d < 0):
            #d = 0
    print(d)"""


"""def min(n,m):
    if(n%2 == 0 and m%2 == 0):
        b = n*(m//2)
    elif(n%2 == 0 and m%2 != 0):
        b = (n*(m//2))+n//2
    elif(n%2 != 0 and m%2 == 0):
        b = n*(m//2)
    else:
        b = (n*(m//2)) + (n-(n//2))
    return(b)
    


for i in range(int(input())):
    n, m = map(int, input().split())
    print(min(n,m))"""
    



"""from collections import defaultdict

def smallest(s1, s2):
    assert s2 != ''
    d = defaultdict(int)
    nneg = [0]  
    def incr(c):
        d[c] += 1
        if d[c] == 0:
            nneg[0] -= 1
    def decr(c):
        if d[c] == 0:
            nneg[0] += 1
        d[c] -= 1
    for c in s2:
        decr(c)
    minlen = len(s1) + 1
    j = 0
    for i in range(len(s1)):
        while nneg[0] > 0:
            if j >= len(s1):
                return minlen
            incr(s1[j])
            j += 1
        minlen = min(minlen, j - i)
        decr(s1[i])
    return minlen
    
# ans = smallest("12222133333332", "123")
# print(ans)

for i in range(int(input())):
    s1= input()
    e = 0
    g = 0
    h = 0
    for i in range(len(s1)):
        if(s1[i] == '1'):
            e += 1
        elif(s1[i] == '2'):
            g += 1
        elif(s1[i] == '3'):
            h += 1
    s2="123"
    
    if(e < 1 or g < 1 or h < 1):
        ans = 0
    else:
        ans= smallest(s1, s2)
    print(ans)"""


"""for i in range(int(input())):
    a, b, c, d = map(int, input().split())
    r = b
    ans = 0
    if(b < a and c < d):
        ans = -1
    else:
        i = 0
        while(r < a):
            r += c - d
            i += 1
        if(i == 0):
            ans = b
        else:
            ans = b + i*c
    print(ans)           

if(d >= c && a >b)
            cout << -1 << endl;
            continue;
        }
        if(a <= b){
            cout << b << endl;
            continue;
        }
        a -= b;
        long int q = c-d;
        if(a % q == 0)
        {
            cout << ((a/q)*c)+b << endl;
        }else{
            cout << (((a/q)+1)*c)+b << endl;
        }"""
"""for i in range(int(input())):
    n = int(input())
    s = list(map(int, input().split()))
    s.sort()
    c = 0
    p = 1
    if(n == 1):
        c = 1
    else:
        
        for i in range(n):
            if(s[i] <= p):
                c += 1
                p = p - s[i] + 1
            else:
                p = p + 1
    print(c)"""



"""res = False
def chkList(lst):
    if len(lst) < 0 : 
        res = True
    res = all(ele == lst[0] for ele in lst)
    return(res)



for i in range(int(input())):
    n = int(input())
    l = list(map(int, input().split()))
    p = l.copy()
    c = 0
    d = []
    if(chkList(l) == True):
        h = len(l)
    else:
        
        h = len(l)
    print(h)"""


"""for i in range(int(input())):
    n = int(input())
    l = list(map(int, input().split()))
    l.sort()
    l.reverse()
    #print(l)
    res = 0
    p = 0
    while(True):
        res += 1
        p = p + l[p]
        if(p >= n):
            break
    print(res)"""
    
"""7017173017"""

    

