To make Yalalovichik even more satisfied and happy, Jafar decided to invent Yalalovichik strings. A string is called a Yalalovichik string if the set of all of its distinct non-empty substrings is equal to the set of all of its distinct non-empty subsequences. 
You are given a string S$S$. You need to find the number of its distinct non-empty substrings which are Yalalovichik strings.
Note: A string A$A$ is called a subsequence of a string B$B$ if A$A$ can be formed by erasing some characters (possibly none) from B$B$. A string A$A$ is called a substring of a string B$B$ if it can be formed by erasing some characters (possibly none) from the beginning of B$B$ and some (possibly none) from the end of B$B$. Two substrings or subsequences are considered different if they are different strings.

-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first line of each test case contains a single integer N=|S|$N = |S|$.
- The second line contains the string S$S$.

-----Output-----
For each test case, print a single line containing one integer — the number of distinct Yalalovichik substrings of S$S$.

-----Constraints-----
- 1≤T≤100$1 \le T \le 100$
- 1≤N≤106$1 \le N \le 10^6$
- the sum of N$N$ over all test cases does not exceed 2⋅106$2 \cdot 10^6$
- S$S$ contains only lowercase English letters

-----Example Input-----
1
3
xxx

-----Example Output-----
3

-----Explanation-----
Example case 1: The distinct Yalalovichik substrings are "x", "xx" and "xxx".

Difficulty: interview

Starter code:

Solutions:
for _ in range(int(input())):
    n,s = int(input()),input().strip()
    previ,num,_s,dic = s[0],0,[],{}
    for i in s:
     if previ == i:
      num+=1
      continue
     _s.append((previ, num))
     if previ not in dic or dic[previ]<num:dic[previ] = num
     previ,num = i,1
    _s.append((previ, num))
    if previ not in dic or dic[previ]<num:dic[previ] = num
    sum1 = sum(dic.values())
    del dic, s
    l,dicc = [i for (i, j) in _s],{}
    congr = [(l[i], l[i+1]) for i in range(len(l)-1)]
    for i in range(len(congr)):
     if congr[i] not in dicc:dicc[congr[i]] = set()
     dicc[congr[i]].add( (_s[i][1], _s[i+1][1]) )       
    sum2,ll = 0,[]
    for i in dicc.keys():
     sortedset,deleted =  sorted(list(dicc[i])),[]
     for k in range(1, len(sortedset)):
      j = sortedset[k]         
      if j[1]>sortedset[k-1][1]:
       ind = k - 1

t = int(input())
while t>0:
    t-=1
    n = int(input())
    s = input().strip()
    previ = s[0]
    num = 0
    _s = []
    dic = {}
    for i in s:
     if previ == i:
      num+=1
      continue
     _s.append((previ, num))
     if previ not in dic or dic[previ]<num:
      dic[previ] = num
     #l.append(previ)
     previ = i
     num  = 1
    _s.append((previ, num))
    if previ not in dic or dic[previ]<num:
      dic[previ] = num

    ##print(_s)
    sum1 = sum(dic.values())
    del dic, s

t = int(input())
while t>0:
    t-=1
    n = int(input())
    s = input().strip()
    previ = s[0]
    num = 0
    _s = []
    dic = {}
    for i in s:
     if previ == i:
      num+=1
      continue
     _s.append((previ, num))
     if previ not in dic or dic[previ]<num:
      dic[previ] = num
     #l.append(previ)
     previ = i
     num  = 1
    _s.append((previ, num))
    if previ not in dic or dic[previ]<num:
      dic[previ] = num

    ##print(_s)
    sum1 = sum(dic.values())
    del dic, s