You are given a permutation p=[p_1, p_2, …, p_n] of integers from 1 to n. Let's call the number m (1 ≤ m ≤ n) beautiful, if there exists two indices l, r (1 ≤ l ≤ r ≤ n), such that the numbers [p_l, p_{l+1}, …, p_r] is a permutation of numbers 1, 2, …, m.

For example, let p = [4, 5, 1, 3, 2, 6]. In this case, the numbers 1, 3, 5, 6 are beautiful and 2, 4 are not. It is because:

  * if l = 3 and r = 3 we will have a permutation [1] for m = 1; 
  * if l = 3 and r = 5 we will have a permutation [1, 3, 2] for m = 3; 
  * if l = 1 and r = 5 we will have a permutation [4, 5, 1, 3, 2] for m = 5; 
  * if l = 1 and r = 6 we will have a permutation [4, 5, 1, 3, 2, 6] for m = 6; 
  * it is impossible to take some l and r, such that [p_l, p_{l+1}, …, p_r] is a permutation of numbers 1, 2, …, m for m = 2 and for m = 4. 



You are given a permutation p=[p_1, p_2, …, p_n]. For all m (1 ≤ m ≤ n) determine if it is a beautiful number or not.

Input

The first line contains the only integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. The next lines contain the description of test cases.

The first line of a test case contains a number n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation p. The next line contains n integers p_1, p_2, …, p_n (1 ≤ p_i ≤ n, all p_i are different) — the given permutation p.

It is guaranteed, that the sum of n from all test cases in the input doesn't exceed 2 ⋅ 10^5.

Output

Print t lines — the answers to test cases in the order they are given in the input. 

The answer to a test case is the string of length n, there the i-th character is equal to 1 if i is a beautiful number and is equal to 0 if i is not a beautiful number.

Example

Input


3
6
4 5 1 3 2 6
5
5 3 1 2 4
4
1 4 3 2


Output


101011
11111
1001

Note

The first test case is described in the problem statement.

In the second test case all numbers from 1 to 5 are beautiful:

  * if l = 3 and r = 3 we will have a permutation [1] for m = 1; 
  * if l = 3 and r = 4 we will have a permutation [1, 2] for m = 2; 
  * if l = 2 and r = 4 we will have a permutation [3, 1, 2] for m = 3; 
  * if l = 2 and r = 5 we will have a permutation [3, 1, 2, 4] for m = 4; 
  * if l = 1 and r = 5 we will have a permutation [5, 3, 1, 2, 4] for m = 5. 
# for t in range(int(input())):
#     s = input()
#     i, j = 0, 0
#     cnt = 0
#     ans = float('inf')
#     dic = {}
#     while j < len(s):
#         if len(dic) < 3:
#             dic[s[j]] = dic.get(s[j], 0) + 1
#         # print(j)
#         # print(dic)
#         while len(dic) == 3:
#             ans = min(ans, j - i + 1)
#             dic[s[i]] -= 1
#             if dic[s[i]] == 0:
#                 del dic[s[i]]
#             i += 1
#
#         j += 1
#     print((0, ans)[ans < float('inf')])


# for t in range(int(input())):
#     n = int(input())
#     s = list(map(int, input().split()))
#     dp = [1] * n
#     for i in range(n):
#         k = 2
#         while (i + 1) * k <= n:
#             j = (i + 1) * k
#             if s[i] < s[j - 1]:
#                 dp[j - 1] = max(dp[j - 1], dp[i] + 1)
#             k += 1
#     print(max(dp))


# for T in range(int(input())):
#     t = input()
#     z, o = 0, 0
#     for ch in t:
#         z = z + 1 if ch == '0' else z
#         o = o + 1 if ch == '1' else o
#     if z > 0 and o > 0:
#         print('01' * len(t))
#     elif o > 0 and not z:
#         print('1' * len(t))
#     else:
#         print('0' * len(t))


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     a.sort()
#     ans = []
#     while a:
#         ans.append(str(a.pop(len(a) // 2)))
#     print(' '.join(ans))


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     cnt = 0
#     p = set()
#     l, r = 0, sum(a)
#     left, right = {}, {}
#     for i in a:
#         right[i] = right.get(i, 0) + 1
#     for i in range(n - 1):
#         l += a[i]
#         left[a[i]] = left.get(a[i], 0) + 1
#         r -= a[i]
#         right[a[i]] = right.get(a[i], 0) - 1
#         if not right[a[i]]:
#             del right[a[i]]
#         j = n - i - 1
#         if (2 + i) * (i + 1) // 2 == l and (j + 1) * j // 2 == r:
#             if len(left) == i + 1 and len(right) == j:
#                 cnt += 1
#                 p.add((i + 1, n - i - 1))
#     print(cnt)
#     if cnt:
#         for el in p:
#             print(*el)


# for t in range(int(input())):
#     n = int(input())
#     G = []
#     taken = [False] * n
#     girl = -1
#     for i in range(n):
#         g = list(map(int, input().split()))
#         k = g[0]
#         single = True
#         for j in range(1, k + 1):
#             if not taken[g[j] - 1]:
#                 taken[g[j] - 1] = True
#                 single = False
#                 break
#         if single:
#             girl = i
#     if girl == -1:
#         print('OPTIMAL')
#     else:
#         print('IMPROVE')
#         print(girl + 1, taken.index(False) + 1)


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     odd, even = [], []
#     for i in range(2 * n):
#         if a[i] % 2:
#             odd.append(i + 1)
#         else:
#             even.append(i + 1)
#     for i in range(n - 1):
#         if len(odd) >= len(even):
#             print(odd.pop(), odd.pop())
#         else:
#             print(even.pop(), even.pop())


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     a.sort()
#     ans, i, j = 0, 0, 1
#     while j < n:
#         if a[i] < a[j]:
#             ans += 1
#             i += 1
#             j += 1
#         else:
#             while j < n and a[i] == a[j]:
#                 i += 1
#                 j += 1
#     print(ans + 1)


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     got = False
#
#     b = 1
#     while not got and b < 2 * n - 1:
#         if b % 2:
#             i, j = (b - 1) // 2, (b + 1) // 2
#         else:
#             i, j = b // 2 - 1, b // 2 + 1
#         left, right = set(a[:i]), set(a[j:])
#         if left & right:
#             got = True
#         b += 1
#     print('YES' if got else 'NO')


# n, m, k = list(map(int, input().split()))
# A = list(map(int, input().split()))
# B = list(map(int, input().split()))
# ans = 0
# a, b = [0], [0]
# for el in A:
#     a.append(a[-1] + el)
# for el in B:
#     b.append(b[-1] + el)
# d = [(i, k//i) for i in range(1, int(k**0.5)+1) if k % i == 0]
# d += [(j, i) for i, j in d if i != j]
# for i in range(n):
#     for j in range(m):
#         for q, p in d:
#             if i + q <= n and j + p <= m:
#                 if a[i + q] - a[i] == q and b[j + p] - b[j] == p:
#                     ans += 1
# print(ans)


# for t in range(int(input())):
#     n = int(input())
#     s = input()
#     dic, se = {s: 1}, {s}
#     for k in range(2, n):
#         p = s[k - 1:] + (s[:k - 1], s[:k - 1][::-1])[(n % 2) == (k % 2)]
#         # print(k, p)
#         if p not in dic:
#             # print(dic, p)
#             dic[p] = k
#             se.add(p)
#     if s[::-1] not in dic:
#         dic[s[::-1]] = n
#         se.add(s[::-1])
#     # print(dic)
#     ans = min(se)
#     print(ans)
#     print(dic[ans])


# for t in range(int(input())):
#     a, b, p = list(map(int, input().split()))
#     s = input()
#     road = [a if s[0] == 'A' else b]
#     st = [0]
#     for i in range(1, len(s) - 1):
#         if s[i] != s[i - 1]:
#             road.append(road[-1] + (a, b)[s[i] == 'B'])
#             st.append(i)
#     # print(road)
#     pay = road[-1]
#     j = 0
#     while pay > p and j < len(st):
#         pay = road[-1] - road[j]
#         j += 1
#     # print(j)
#     print(st[j] + 1 if j < len(st) else len(s))


# for t in range(int(input())):
#     n, x, y = list(map(int, input().split()))
#     print(max(1, min(x + y - n + 1, n)), min(n, x + y - 1))


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     print(' '.join(map(str, sorted(a, reverse=True))))


# s = input()
# open, close = [], []
# i = 0
# for i in range(len(s)):
#     if s[i] == '(':
#         open.append(i)
#     else:
#         close.append(i)
# i, j = 0, len(close) - 1
# ans = []
# while i < len(open) and j >= 0 and open[i] < close[j]:
#     ans += [open[i] + 1, close[j] + 1]
#     i += 1
#     j -= 1
# ans.sort()
# print('0' if not ans else '1\n{}\n{}'.format(len(ans), ' '.join([str(idx) for idx in ans])))


import collections
# n, m = list(map(int, input().split()))
# a = list(input() for i in range(n))
# dic = {}
# for w in a:
#     dic[w] = dic.get(w, 0) + 1
# l, r = '', ''
# for i in range(n):
#     for j in range(i + 1, n):
#         # print(i, j, a)
#         if a[i] == a[j][::-1] and dic[a[i]] and dic[a[j]]:
#             l += a[i]
#             r = a[j] + r
#             dic[a[i]] -= 1
#             dic[a[j]] -= 1
# c = ''
# for k, v in dic.items():
#     if v and k == k[::-1]:
#         if c and c[-m] == k or not c:
#             c += k
# print(f'{len(l) + len(c) + len(r)}\n{l + c + r}')


# for t in range(int(input())):
#     n, g, b = list(map(int, input().split()))
#     d = n // 2 + n % 2
#     full, inc = divmod(d, g)
#     ans = (g + b) * (full - 1, full)[inc > 0] + (g, inc)[inc > 0]
#     print(ans if ans >= n else n)


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     a.sort()
#     print(a[n] - a[n - 1])


# for t in range(int(input())):
#     n, x = list(map(int, input().split()))
#     s = input()
#     cntz = s.count('0')
#     total = 2 * cntz - n
#     bal = 0
#     ans = 0
#     for i in range(n):
#         if not total:
#             if bal == x:
#                 ans = -1
#         elif not abs(x - bal) % abs(total):
#             if (x - bal) // total >= 0:
#                 ans += 1
#         bal += 1 if s[i] == '0' else -1
#     print(ans)


# n = int(input())
# ans = 0
# for i in range(1, n + 1):
#     ans += 1 / i
# print(ans)


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     p, s = 0, n - 1
#     for i in range(n):
#         if a[i] < i:
#             break
#         p = i
#     for i in range(n - 1, -1, -1):
#         if a[i] < n - i - 1:
#             break
#         s = i
#     print('Yes' if s <= p else 'No')


# n, k = list(map(int, input().split()))
# a = [input() for i in range(n)]
# c = set(a)
# b = set()
# for i in range(n):
#     for j in range(i + 1, n):
#         third = ''
#         for c1, c2 in zip(a[i], a[j]):
#             if c1 == c2:
#                 third += c1
#             else:
#                 if c1 != 'S' and c2 != 'S':
#                     third += 'S'
#                 elif c1 != 'E' and c2 != 'E':
#                     third += 'E'
#                 else:
#                     third += 'T'
#         if third in c:
#             b.add(frozenset([a[i], a[j], third]))
# print(len(b))


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     total, curr = sum(a), 0
#     ans, i, start = 'YES', 0, 0
#     while ans == 'YES' and i < n:
#         if curr > 0:
#             curr += a[i]
#         else:
#             curr = a[i]
#             start = i
#         # print(curr, i, start, total)
#         if i - start + 1 < n and curr >= total:
#             ans = 'NO'
#         i += 1
#     print(ans)


# for t in range(int(input())):
#     n, p, k = list(map(int, input().split()))
#     a = list(map(int, input().split()))
#     a.sort(reverse=True)
#     odd, even = 0, 0
#     i, j = len(a) - 1, len(a) - 2
#     curr = 0
#     while curr < p and i >= 0:
#         curr += a[i]
#         if curr <= p:
#             odd += 1
#         i -= 2
#     curr = 0
#     while curr < p and j >= 0:
#         curr += a[j]
#         if curr <= p:
#             even += 1
#         j -= 2
#     print(max(odd * 2 - 1, even * 2))


# for t in range(int(input())):
#     s, c = input().split()
#     s = list(ch for ch in s)
#     sor = sorted(s)
#     for i in range(len(s)):
#         if s[i] != sor[i]:
#             j = max(j for j, v in enumerate(s[i:], i) if v == sor[i])
#             s = s[:i] + [s[j]] + s[i + 1:j] + [s[i]] + s[j + 1:]
#             break
#     s = ''.join(s)
#     print(s if s < c else '---')


# for t in range(int(input())):
#     n, s = list(map(int, input().split()))
#     a = list(map(int, input().split()))
#     if sum(a) <= s:
#         print(0)
#     else:
#         curr, i, j = 0, 0, 0
#         for i in range(n):
#             if a[i] > a[j]:
#                 j = i
#             s -= a[i]
#             if s < 0:
#                 break
#         print(j + 1)


# for t in range(int(input())):
#     a, b = list(map(int, input().split()))
#     a, b = (b, a) if b > a else (a, b)
#     if not ((1 + 8 * (a - b))**0.5 - 1) % 2 and ((1 + 8 * (a - b))**0.5 - 1) // 2 >= 0:
#         ans = ((1 + 8 * (a - b))**0.5 - 1) // 2
#         print(int(ans))
#     else:
#         n1 = int(((1 + 8 * (a - b))**0.5 - 1) // 2) + 1
#         while (n1 * (n1 + 1) // 2) % 2 != (a - b) % 2:
#             n1 += 1
#         print(n1)


# for t in range(int(input())):
#     n = int(input())
#     a = list(map(int, input().split()))
#     a.sort()
#     ans = 0
#     l = 0
#     dic = {}
#     for i in range(n - 1, -1, -1):
#         if not a[i] % 2:
#             l, r = 0, 30
#             while l < r:
#                 m = (l + r) // 2
#                 # print(l, r, m, a[i] % 2**m)
#                 if a[i] % 2**m:
#                     r = m
#                 else:
#                     l = m + 1
#             dic[a[i] // 2**(l - 1)] = max(dic.get(a[i] // 2**(l - 1), 0), l - 1)
#     print(sum(list(dic.values())))


# n = int(input())
# s = input()
# b = s.count('B')
# w = n - b
# if b % 2 and w % 2:
#     print(-1)
# elif not b or not w:
#     print(0)
# else:
#     ans = []
#     if not b % 2:
#         for i in range(n - 1):
#             if s[i] != 'W':
#                 ans += [str(i + 1)]
#                 s = s[:i] + 'W' + 'BW'[s[i + 1] == 'B'] + s[i + 2:]
#     elif not w % 2:
#         for i in range(n - 1):
#             if s[i] != 'B':
#                 ans += [str(i + 1)]
#                 s = s[:i] + 'B' + 'WB'[s[i + 1] == 'W'] + s[i + 2:]
#     print(len(ans))
#     print(' '.join(ans))


# n, m = list(map(int, input().split()))
# a = list(map(int, input().split()))
# b = list(map(int, input().split()))
# b.sort()
# ans = float('inf')
# for i in range(n):
#     x = (b[0] - a[i]) % m
#     ax = []
#     for j in range(n):
#         ax.append((a[j] + x) % m)
#     if b == sorted(ax):
#         ans = min(ans, x)
# print(ans)


for t in range(int(input())):
    n = int(input())
    ans = [1] + [0] * (n - 1)
    p = list(map(int, input().split()))
    i, j, curr, m = p.index(1), 1, 1, 1
    l, r = i, i
    while l >= 0 and r < n:
        if l and curr + p[l - 1] == (m + 2) * (m + 1) // 2:
            ans[m] = 1
            curr += p[l - 1]
            l -= 1

        elif r + 1 < n and curr + p[r + 1] == (m + 2) * (m + 1) // 2:
            ans[m] = 1
            curr += p[r + 1]
            r += 1
        else:
            if l and r + 1 < n:
                curr, l, r = ((curr + p[l - 1], l - 1, r),
                              (curr + p[r + 1], l, r + 1))[p[r + 1] < p[l - 1]]
            elif not l and r + 1 < n:
                curr, l, r = curr + p[r + 1], l, r + 1
            elif r + 1 == n and l:
                curr, l, r = curr + p[l - 1], l - 1, r
            else:
                break
        m += 1
    print(''.join([str(i) for i in ans]))
