import math
from fractions import Fraction



factorials = [1]
N = 200
for i in range(N + 5):
    factorials.append(factorials[-1] * (i + 1))


def C(n, k):
    return factorials[n] // factorials[k] // factorials[n - k]


def sign(n):
    if n % 2 == 0:
        return 1
    return -1


poly = [[Fraction(0, 1), Fraction(1, 1)]]
pp = [[Fraction(1, 1)]]
for i in range(1, N):
    cur = [Fraction(0, 1) for j in range(i + 2)]
    cur[i + 1] += 1
    for j in range(1, i + 1):
        for it in range(len(poly[i - j])):
            cur[it] += C(i + 1, j + 1) * sign(j + 1) * poly[i - j][it]
    for j in range(len(cur)):
        cur[j] /= i + 1
    poly.append(cur)

    cur = [Fraction(0, 1) for j in range(len(pp[-1]) + 2)]
    for j in range(len(pp[-1])):
        cur[j] -= pp[-1][j]
        cur[j + 1] += pp[-1][j] / 2
        cur[j + 2] += pp[-1][j] / 2
    pp.append(cur)
#print(pp)

ff = [[Fraction(1, 1)]]
FF = []

K = 5
MX = 613

for i in range(K):
    cur = [Fraction(0, 1) for j in range(len(ff[-1]) + 1)]
    for j in range(len(ff[-1])):
        for k in range(len(poly[j])):
            cur[k] += ff[-1][j] * poly[j][k]
    FF.append(cur)
    if i == K - 1:
        break
    cur = [Fraction(0, 1) for j in range(len(FF[-1]) * 2)]
    for j in range(len(FF[-1])):
        for k in range(len(pp[j])):
            cur[k] += FF[-1][j] * pp[j][k]
    ff.append(cur)


prec_f = []
prec_F = []
prec = []


def P(n) -> int:
    D = 1 + 8 * n
    k = (int(math.isqrt(D)) - 1) // 2
    while (k + k + 3) * (k + k + 3) <= D:
        k += 1
    while (k + k + 1) * (k + k + 1) > D:
        k -= 1
    return k


good = [0, 1]
M = 1000
for i in range(2, M + 5):
    good.append(good[-1] + good[P(i)])

for i in range(K):
    cur = []
    for x in range(MX):
        s = Fraction(0, 1)
        y = 1
        for k in range(len(ff[i])):
            s += y * ff[i][k]
            y *= x
        cur.append(s)
    prec_f.append(cur)
    cur = []
    for x in range(MX):
        s = Fraction(0, 1)
        y = 1
        for k in range(len(FF[i])):
            s += y * FF[i][k]
            y *= x
        cur.append(s)
    prec_F.append(cur)
    cur = [0]
    s = 0
    for x in range(1, MX):
        s += prec_f[i][x] * good[P(x)]
        cur.append(s)
    prec.append(cur)


def f(d, n):
    if d == 0:
        return 1
    if d < len(ff):
        if n < MX:
            return prec_f[d][n]
        s = Fraction(0, 1)
        x = 1
        for i in range(len(ff[d])):
            s += ff[d][i] * x
            x *= n
        return s
    return F(d - 1, (n * (n + 1)) // 2 - 1)


def F(d, n):
    if d == 0:
        return n
    if d < len(FF):
        if n < MX:
            return prec_F[d][n]
        s = Fraction(0, 1)
        x = 1
        for i in range(len(FF[d])):
            s += FF[d][i] * x
            x *= n
        return s
    s = 0
    for i in range(1, n + 1):
        s += f(d, i)
    return s


def solve(n: int, d = 0):
    if n == 1:
        return f(d, 1)
    if d < len(prec) and n < MX:
        return prec[d][n]
    to = P(n)
    return F(d, n) * solve(to) - solve(to, d + 1)


"""


def stupid(n):
    return good[n]
"""



t = int(input())


while t > 0:
    n = int(input())
    #n = 10000000000000000000000000000000000000000 - t
    #n = M - t + 1
    cur = solve(n)
    #print(type(cur))
    print(cur)
    #cur -= stupid(n)
    #assert cur == 0
    t -= 1