'''python
from qiskit import QuantumCircuit, QuantumRegister
import math
import numpy as n

def PS_oracle(n, L, theta):

    qc = QuantumCircuit(n)
    # Write your code here:
    #for i in range(n):
    #   qc.h(i)

    binary = bin(L)
    ctrl_state = binary[-1:1:-1]

    print(ctrl_state)

    ctrl_state = ctrl_state + (n - len(ctrl_state))*'0'
    print(ctrl_state)

    print(ctrl_state[0])

    if n > 1:

        if ctrl_state[0] == '0':
            ctrl_state = ctrl_state[-1:0:-1]
            print(ctrl_state)
            qc.x(0)
            qc.mcp(theta, control_qubits= [i for i in range(1,n)] , ctrl_state = ctrl_state,target_qubit= 0)
            qc.x(0)

        else :
            ctrl_state = ctrl_state[-1:0:-1]
            print(ctrl_state)
            qc.mcp(theta, control_qubits= [i for i in range(1,n)] , ctrl_state = ctrl_state,target_qubit= 0)

    #qc.measure_all()
    else :
        if L == 0:
            qc.x(0)
        qc.p(theta , 0)
        if L == 0:
            qc.x(0)

    return qc

def qft(n):
    qc = QuantumCircuit(n)

    thetas = []
    for k in range(0, 1+n):
        thetas.append(2 * math.pi / (2**k))

    for idx in range(0, n):
        qc.h(n-1-idx)
        for jdx in range(idx+1, n):
            thetaidx = jdx - idx + 1
            qc.cp(thetas[thetaidx], n-1-jdx, n-1-idx)

    for idx in range(0, n//2):
        qc.swap(idx, n-idx-1)

    return qc

def solve(n: int, m: int, L: int, S: list[int], theta: float) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:

    qc.h(y)
    for idx in range(0, n):
        for jdx in range(0, m):
            theta = 2 * math.pi * S[idx] * (2**jdx) / (2**m)
            qc.cp(theta, x[idx], y[jdx])

    qc = qc.compose(qft(m).inverse(), y)
    qc = qc.compose(PS_oracle(m, L, theta), y)

    qc = qc.compose(qft(m), y)

    for idx in range(0, n):
        for jdx in range(0, m):
            theta = -2 * math.pi * S[idx] * (2**jdx) / (2**m)
            qc.cp(theta, x[idx], y[jdx])

    qc.h(y)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
import math
import numpy as n

def PS_oracle(n, L, theta):

    qc = QuantumCircuit(n)
    # Write your code here:
    #for i in range(n):
    #   qc.h(i)

    binary = bin(L)
    ctrl_state = binary[-1:1:-1]

    print(ctrl_state)

    ctrl_state = ctrl_state + (n - len(ctrl_state))*'0'
    print(ctrl_state)

    print(ctrl_state[0])

    if n > 1:

        if ctrl_state[0] == '0':
            ctrl_state = ctrl_state[-1:0:-1]
            print(ctrl_state)
            qc.x(0)
            qc.mcp(theta, control_qubits= [i for i in range(1,n)] , ctrl_state = ctrl_state,target_qubit= 0)
            qc.x(0)

        else :
            ctrl_state = ctrl_state[-1:0:-1]
            print(ctrl_state)
            qc.mcp(theta, control_qubits= [i for i in range(1,n)] , ctrl_state = ctrl_state,target_qubit= 0)

    #qc.measure_all()
    else :
        if L == 0:
            qc.x(0)
        qc.p(theta , 0)
        if L == 0:
            qc.x(0)

    return qc

def qft(n):
    qc = QuantumCircuit(n)

    thetas = []
    for k in range(0, 1+n):
        thetas.append(2 * math.pi / (2**k))

    for idx in range(0, n):
        qc.h(n-1-idx)
        for jdx in range(idx+1, n):
            thetaidx = jdx - idx + 1
            qc.cp(thetas[thetaidx], n-1-jdx, n-1-idx)

    for idx in range(0, n//2):
        qc.swap(idx, n-idx-1)

    return qc

def solve(n: int, m: int, L: int, S: list[int], theta: float) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:

    qc.h(y)
    for idx in range(0, n):
        for jdx in range(0, m):
            theta = 2 * math.pi * S[idx] * (2**jdx) / (2**m)
            qc.cp(theta, x[idx], y[jdx])

    qc = qc.compose(qft(m).inverse(), y)
    qc = qc.compose(PS_oracle(m, L, theta), y)

    qc = qc.compose(qft(m), y)

    for idx in range(0, n):
        for jdx in range(0, m):
            theta = -2 * math.pi * S[idx] * (2**jdx) / (2**m)
            qc.cp(theta, x[idx], y[jdx])

    qc = qc.compose(qft(m).inverse(), y)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
import math

from qiskit import QuantumCircuit

def B2(n: int, L: int, theta: float) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    for i in range(n):
        if not (L>>i & 1):
            qc.x(i)
    if n==1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(n-1)), n-1)
    for i in range(n):
        if not (L>>i & 1):
            qc.x(i)
    return qc

def QFT(n: int) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    for i in range(n):
        qc.h(n-i-1)
        for j in range(1, n-i):
            qc.cp(math.pi/2**j, n-i-j-1, n-i-1)
    for i in range(n//2):
        qc.swap(i, n-i-1)
    return qc

def IQFT(n: int) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    for i in range(n):
        qc.h(n-i-1)
        for j in range(1, n-i):
            qc.cp(-math.pi/2**j, n-i-j-1, n-i-1)
    for i in range(n//2):
        qc.swap(i, n-i-1)
    return qc

def solve(n: int, m: int, L: int, S: list[int], theta: float) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:
    for j in range(m):
        qc.h(y[j])
        # Oracle B5
        for i in range(n):
            qc.cp(2*math.pi*S[i]*2**j/2**m, y[j], x[i])
    # IQFT
    qc.compose(IQFT(m), y, inplace=True)

    qc.compose(B2(m, L, theta), y, inplace=True)

    # QFT
    qc.compose(QFT(m), y, inplace=True)

    for j in range(m):
        # Oracle B5(minus)
        for i in range(n):
            qc.cp(-2*math.pi*S[i]*2**j/2**m, y[j], x[i])

    # IQFT
    qc.compose(IQFT(m), y, inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit import Gate
import numpy as np

def solve(n: int, m: int, L: int, S: list[int], theta: float) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:
    def compute_f(x_state):
        return sum(S[i] * int(x_state[i]) for i in range(n))

    # Iterate over all possible states for the n qubits
    for i in range(2 ** n):
        x_state = [int(bit) for bit in format(i, f'0{n}b')]
        f_x = compute_f(x_state)
        f_x_mod = f_x % (2 ** m)

        # Apply the phase based on the condition
        if f_x_mod == L:
            # Apply phase shift
            qc.u1(theta, y[0])  # Applying phase gate U1 is equivalent to exp(i*theta) for one qubit

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from math import pi

def solve(n: int, m: int, L: int, S: list[int], theta: float) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    # Write your code here:
    for i in range(n):
        for j in range(m):
            angle = pi * S[i] / (2**j)
            qc.cu1(angle, i, n+j)

    # Compare f(x) with L (mod 2^m)
    # ... (Implement comparison logic here)

    # Apply phase shift if f(x) = L (mod 2^m)
    # ... (Implement controlled phase gate based on comparison result)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
import math

# from qiskit.quantum_info import Statevector

def quantum_fourier_transform(n: int) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    for i in range(n-1, -1, -1):
        qc.h(i)
        for j in range(i-1, -1, -1):
            qc.cp(2*math.pi/(2**(i-j+1)), j, i)

    i = 0
    while i<n-i-1:
        qc.swap(i, n-i-1)
        i += 1

    return qc

def b7(n: int, m: int, S: list[int]) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)
    qc.compose(quantum_fourier_transform(m), y, inplace=True)
    for j in range(m):
        for i in range(n):
            qc.cp(2*math.pi*S[i]/(2**m)*(2**j), x[i], y[j])
    qc.compose(quantum_fourier_transform(m).inverse(), y, inplace=True)

    return qc

def b2(n: int, L: int, theta: float) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    for i in range(n):
        if ((L>>i)&1)==0:
            qc.x(i)
    if n==1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(n-1)), n-1)
    for i in range(n):
        if ((L>>i)&1)==0:
            qc.x(i)
    return qc

def solve(n: int, m: int, L: int, S: list[int], theta: float) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(m)
    qc = QuantumCircuit(x, y)

    # init = [0]*(2**(n+m))
    # init[3] = 1
    # qc.initialize(init)

    # Write your code here:

    qc.compose(b7(n, m, S), inplace=True)
    qc.compose(b2(m, L, theta), y, inplace=True)
    qc.compose(b7(n, m, S).inverse(), inplace=True)

    return qc

# if __name__ == "__main__":
#     qc = solve(2, 2, 3, [1, 2], 3.14159)
#     print(Statevector(qc))
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    qc.mcp(math.pi/3, list(range(0, n-1)), n-1)
    qc.x(range(n))

    return qc

def compose(u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:

    u0 = U
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(u0, rs, rt)
    u2 = compose(u1, rs, rt)
    u3 = compose(u2, rs, rt)
    u3 = compose(u2, rs, rt)

    return u3
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    qc.mcp(math.pi/3, list(range(0, n-1)), n-1)
    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:

    u0 = U
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u3 = compose(n, u2, rs, rt)

    return u3
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    qc.mcp(math.pi/3, list(range(0, n-1)), n-1)
    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:

    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u3 = compose(n, u2, rs, rt)

    return u3
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    qc.mcp(math.pi/3, list(range(0, n-1)), n-1)
    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:

    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:

    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.5:
        def UInv():
            return U().inverse()

        return solve(n, 1/P, UInv, R)

    qc = QuantumCircuit(n)
    # Write your code here:

    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.5:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4.inverse()

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rt, rs)
    u2 = compose(n, u1, rt, rs)
    u3 = compose(n, u2, rt, rs)
    u4 = compose(n, u3, rt, rs)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.5:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rt, rs)
    u2 = compose(n, u1, rt, rs)
    u3 = compose(n, u2, rt, rs)
    u4 = compose(n, u3, rt, rs)

    return u4.inverse()

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 1.0/4:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U().inverse()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rt, rs)
    u2 = compose(n, u1, rt, rs)
    u3 = compose(n, u2, rt, rs)
    u4 = compose(n, u3, rt, rs)

    return u4.inverse()

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.5:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U().inverse()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rt, rs)
    u2 = compose(n, u1, rt, rs)
    u3 = compose(n, u2, rt, rs)
    u4 = compose(n, u3, rt, rs)

    return u4.inverse()

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))
    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 1/np.sqrt(2):
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U().inverse()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rt, rs)
    u2 = compose(n, u1, rt, rs)
    u3 = compose(n, u2, rt, rs)
    u4 = compose(n, u3, rt, rs)

    return u4.inverse()

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(math.pi/3, 0)
    else:
        qc.mcp(math.pi/3, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    return solve1(n, U, R)

    if P < 0.5:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U().inverse()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rt, rs)
    u2 = compose(n, u1, rt, rs)
    u3 = compose(n, u2, rt, rs)
    u4 = compose(n, u3, rt, rs)

    return u4.inverse()

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(theta, n):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    return solve1(n, U, R)

    if P < 0.5:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U()
    rs = get_rs(n, -math.pi/3)
    rt = R(-math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    return solve1(n, U, R)

    if P < 0.5:
        return solve1(n, U, R)
    else:
        return solve2(n, U, R)

# make w to 0, inverse
def solve1(n, U, R):
    u0 = U()
    rs = get_rs(n, -math.pi/3)
    rt = R(-math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4

def solve2(n, U, R):
    u0 = U()
    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = U()
    rs = get_rs(n, math.pi/2)
    rt = R(math.pi/2)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u0
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = U()
    rs = get_rs(n, math.pi/2)
    rt = R(math.pi/2)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = U()
    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)
    u5 = compose(n, u4, rs, rt)

    return u5
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = U()
    rs = R(math.pi/3)
    rt = get_rs(n, math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4.inverse()
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = U().inverse()
    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = QuantumCircuit(n)
    u0.h(range(n))

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    u0 = QuantumCircuit(n)
    u0.ry(1, range(n))
    u0.h(range(n))

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.3:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.2:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.1:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if 0.4 < P < 0.5:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    # Apply U to the initial state |0>
    qc.compose(U(), inplace=True)

    # Calculate the optimal number of repetitions of R(θ)
    # Grover-like amplification strategy
    theta = np.arccos(np.sqrt(P))
    k = int(np.round(np.pi / (4 * theta)))

    for _ in range(min(k, 100)):
        qc.compose(R(2 * theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
     qc.compose(U(), inplace=True)
      theta = 2 * 3.141592653589793 * 0.5
    qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
     qc.compose(U(), inplace=True)

    theta = 2 * P
    for _ in range(100):
        qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
     ancilla_qubits = QuantumRegister(n)
    qc.add_register(ancilla_qubits)

    qc.compose(U(), inplace=True)

    qc.append(QFTInverse(n), ancilla_qubits)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import QFTInverse

def U():

    pass

def R(theta):

    pass

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    ancilla_qubits = QuantumRegister(n)
    qc.add_register(ancilla_qubits)

    qc.compose(U(), inplace=True)

    qc.append(QFTInverse(n), ancilla_qubits)

    return qc

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import QFTInverse

def U():
    #
    pass

def R(theta):

    pass

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    ancilla_qubits = QuantumRegister(n)
    qc.add_register(ancilla_qubits)

    qc.compose(U(), inplace=True)

    qc.append(QFTInverse(n), ancilla_qubits)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)

    # Apply the R(θ) gate
    theta = 2 * np.arccos(np.sqrt(P))  # Compute θ such that sin^2(θ/2) = P
    qc.compose(R(theta), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    # Apply the unitary gate U to the quantum circuit
    qc.compose(U(), inplace=True)

    # Choose theta for the R(theta) gate to maximize overlap
    theta = np.angle(1 - np.sqrt(P))  # Example choice, you may need to optimize this

    # Apply the parametric gate R(theta)
    qc.compose(R(theta), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    # Apply the unitary gate U to the quantum circuit
    qc.compose(U(), inplace=True)

    # Choose theta for the R(theta) gate to maximize overlap
    theta = np.angle(1 - np.sqrt(P))  # Example choice, you may need to optimize this

    # Apply the parametric gate R(theta)
    qc.compose(R(theta), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)

    theta = np.arccos(1 - P) * 2  # Derived from P for optimal θ
    qc.compose(R(theta), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit

from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, angle):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(angle, 0)
    else:
        qc.mcp(angle, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return qc
'''


'''python
from qiskit import QuantumCircuit

from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    # Apply U gate once
    qc.compose(U(), inplace=True)

    # Iteratively apply R(theta) gate with incremental phase shifts
    for _ in range(100):
        qc.compose(R(0.01), inplace=True)  # Small phase shift for iterative approach
        qc.compose(U(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Apply U gate first to move the initial state
    qc.compose(U(), inplace=True)

    # Apply the Grover-like iteration to refine the state towards |omega>
    # Here we use a loop with the max allowed number of R applications, but this could be tuned
    for _ in range(100):
        qc.compose(R(0), inplace=True)  # Apply R(θ) with given θ
        qc.compose(U().inverse(), inplace=True)  # Apply U inverse
        qc.compose(R(0), inplace=True)  # Apply R(θ) again
        qc.compose(U(), inplace=True)  # Apply U again
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Apply U to create an initial superposition
    qc.compose(U(), inplace=True)

    # Apply R(θ) once or a few times to refine the state
    qc.compose(R(0), inplace=True)

    # Apply the inverse of U to bring the state closer to |ω>
    qc.compose(U().inverse(), inplace=True)

    # Apply R(θ) again if needed (depending on the results of the first application)
    qc.compose(R(0), inplace=True)

    # A final application of U to finalize the state preparation
    qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def get_rs(n, theta):
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(0, n-1)), n-1)

    qc.x(range(n))

    return qc

def compose(n, u, rs, rt):
    qc = QuantumCircuit(n)

    qc.compose(u, inplace=True)
    qc.compose(rt, inplace=True)
    qc.compose(u.inverse(), inplace=True)
    qc.compose(rs, inplace=True)
    qc.compose(u, inplace=True)

    return qc

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""
def solve(n: int, P: float, U, R) -> QuantumCircuit:
    if P < 0.05:
        u0 = QuantumCircuit(n)
        u0.ry(1, range(n))
        u0.h(range(n))
    else:
        u0 = U()

    rs = get_rs(n, math.pi/3)
    rt = R(math.pi/3)

    u1 = compose(n, u0, rs, rt)
    u2 = compose(n, u1, rs, rt)
    u3 = compose(n, u2, rs, rt)
    u4 = compose(n, u3, rs, rt)

    return u4
'''


'''python
import math

from qiskit import QuantumCircuit
from scipy.special import eval_chebyt

def R_0(n: int, theta: float) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    qc.x(range(n))

    if n == 1:
        qc.p(theta, 0)
    else:
        qc.mcp(theta, list(range(n - 1)), n - 1)

    qc.x(range(n))

    return qc

# Calculate the minimum number of query L
def calculate_L(delta: float, lambda_: float) -> int:
    L = int(math.ceil(math.log(2 / delta) / math.sqrt(lambda_)))

    # Check if L is odd
    if L % 2 == 0:
        L += 1

    return L

def calculate_gamma(L: int, delta: float) -> float:
    # Calculate the Chebyshev polynomial T_{1/L}(1/δ)
    chebyshev_value = eval_chebyt(1 / L, 1 / delta)

    # γ is the inverse of the Chebyshev value
    return 1 / chebyshev_value

# Define the fixed-point Grover's algorithm
def fixed_point_grover(n: int, delta: float, lambda_: float, U, R) -> QuantumCircuit:
    L = calculate_L(delta, lambda_)

    # Calculate the angles for Grover's iteration
    gamma = calculate_gamma(L, delta)
    angles = [
        -2 * math.atan(1 / (math.tan(2 * math.pi * j / L) * math.sqrt(1 - gamma**2)))
        for j in range(1, L // 2 + 1)
    ]

    qc = QuantumCircuit(n)
    qc.compose(U(), inplace=True)
    for alpha, beta in zip(angles, reversed(angles)):
        qc.compose(R(beta), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        qc.compose(R_0(n, alpha), inplace=True)
        qc.compose(U(), inplace=True)

    return qc

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    delta = 0.01
    lambda_ = P
    return fixed_point_grover(n, delta, lambda_, U, R)
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Step 1: Apply the gate U to the initial state |0>
    qc.compose(U(), inplace=True)

    # Step 2: Determine the number of times to apply R(theta)
    # We will apply R(theta) multiple times to converge to |omega>
    # The number of applications can be adjusted based on P
    num_R_applications = min(100, int(100 * (1 - P)))  # Example heuristic

    # Step 3: Apply R(theta) multiple times
    theta = 0.1  # Example value for theta, can be adjusted
    for _ in range(num_R_applications):
        qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Initialize the state |omega> using U and R gates
    qc.compose(U(), inplace=True)
    qc.compose(R(0), inplace=True)  # Initialize |omega> with R(0)

    # Apply R(theta) gate to prepare the state |omega>
    for _ in range(100):
        qc.compose(R(0.01), inplace=True)  # Apply R(0.01) gate iteratively

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)

    theta = np.arccos(np.sqrt(P))
    for _ in range(10):
        qc.compose(R(theta), inplace=True)

    qc.compose(U().inverse(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)

    theta = np.arccos(np.sqrt(P))
    for _ in range(10):
        qc.compose(R(theta), inplace=True)

    qc.compose(U().inverse(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(),inplace=True)
    theta = np.arccos(np.sqrt(p))*2

    m = int(np.pi/2/theta - 0.5)
    for i in range(m):
        qc.compose(R(np.pi), inplace=True)

        qc.compose(U(),inplace=True)
        qc.x(range(n))
        qc.h(n-1)
        qc.mcx(list(range(n-1)), n-1)
        qc.h(n-1)
        qc.x(range(n))
        qc.compose(U(),inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Calculate the number of iterations
    num_iterations = math.floor(math.pi / (4 * math.asin(math.sqrt(P))))

    # Apply U to prepare the initial superposition
    qc.compose(U(), inplace=True)

    # Amplitude amplification
    for _ in range(num_iterations):
        # Apply R(pi) which is equivalent to the oracle
        qc.compose(R(math.pi), inplace=True)

        # Apply U
        qc.compose(U(), inplace=True)

        # Apply R(0) which is equivalent to the diffusion operator
        qc.compose(R(0), inplace=True)

        # Apply U inverse
        qc.compose(U().inverse(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Apply U to prepare the initial state
    qc.compose(U(), inplace=True)

    # Calculate the phase for R
    theta = 2 * math.asin(math.sqrt(P))

    # Apply phase estimation
    num_iterations = int(math.pi / (2 * theta))

    for _ in range(num_iterations):
        qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Calculate the phase for R
    theta = 2 * math.asin(math.sqrt(P))

    # Calculate the number of iterations
    L = min(math.pi / (2 * theta), 100)  # Ensure we don't exceed 100 applications
    m = math.ceil(math.log(L, 2))  # Number of bits for phase estimation

    # Apply U to prepare the initial state
    qc.compose(U(), inplace=True)

    # Fixed-Point Quantum Search
    for k in range(m):
        # Apply controlled rotation
        angle = 2 * math.pi / (2 ** (k + 1))
        for j in range(2**k):
            qc.compose(R(angle), inplace=True)

        # Apply U†
        qc.compose(U().inverse(), inplace=True)

        # Apply controlled-Z
        qc.z(0)

        # Apply U
        qc.compose(U(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Apply U to prepare the initial state
    qc.compose(U(), inplace=True)

    # Calculate the optimal number of iterations
    m = math.floor(math.pi / (4 * math.asin(math.sqrt(P))) - 0.5)
    m = min(m, 50)  # Ensure we don't exceed 100 applications of R

    # Apply amplitude amplification
    for _ in range(m):
        # Apply R(π)
        qc.compose(R(math.pi), inplace=True)

        # Apply U†
        qc.compose(U().inverse(), inplace=True)

        # Apply R(π)
        qc.compose(R(math.pi), inplace=True)

        # Apply U
        qc.compose(U(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

"""You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Write your code here:

    # Apply U to prepare the initial state
    qc.compose(U(), inplace=True)

    # Calculate the optimal number of iterations
    m = math.floor(math.pi / (4 * math.asin(math.sqrt(P))) - 0.5)
    m = min(m, 50)  # Ensure we don't exceed 100 applications of R

    # Apply amplitude amplification
    for _ in range(m):
        # Apply R(π)
        qc.compose(R(math.pi), inplace=True)

        # Apply U†
        qc.compose(U().inverse(), inplace=True)

        # Apply R(π)
        qc.compose(R(math.pi), inplace=True)

        # Apply U
        qc.compose(U(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    import math

    qc.compose(U(), inplace=True)

    m = min(int(math.pi / (4 * math.asin(math.sqrt(P))) - 0.5), 50)

    for _ in range(m):
        qc.compose(R(math.pi), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        qc.compose(R(math.pi), inplace=True)
        qc.compose(U(), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    import math

    qc.compose(U(), inplace=True)

    theta = 2 * math.asin(math.sqrt(P))
    iterations = min(int(math.pi / (2 * theta)), 100)

    for _ in range(iterations):
        qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    import math

    # Apply U to prepare the initial state
    qc.compose(U(), inplace=True)

    # Calculate the number of iterations
    m = min(int(1 / math.sqrt(P)), 100)

    # Apply phase estimation
    for k in range(m):
        theta = 2 * math.pi / (2 ** (k + 1))
        qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Apply U to the quantum circuit
    qc.compose(U(), inplace=True)

    # Choose theta based on P
    # Note: We need to derive or choose theta such that the projection yields the probability P.
    # This is often done by solving equations or approximations, but for simplicity,
    # we will use a fixed theta as an example. This will need adjustment based on P.
    # We use a placeholder theta here; you need to compute this based on the problem requirements.
    theta = np.arccos(np.sqrt(P))  # Example, adjust according to exact requirements

    # Apply R(theta) to the quantum circuit
    qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Apply U to the quantum circuit
    qc.compose(U(), inplace=True)

    # Calculate theta based on P
    # We solve for theta where:
    # P = |⟨ω|U|0⟩|^2
    # For simplicity, we'll use a direct calculation for theta
    # which is typically derived from the problem specifics. Here, a generic example.
    # Ensure the calculation matches the probability requirement.

    # Example: theta calculation
    theta = 2 * np.arccos(np.sqrt(P))

    # Apply R(theta) to the quantum circuit
    qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # Apply U to the quantum circuit
    qc.compose(U(), inplace=True)

    # Compute theta
    # We use P to determine theta for the R(theta) gate.
    # Since theta needs to match the probability P, we use:
    # theta = 2 * arccos(sqrt(P))
    theta = 2 * np.arccos(np.sqrt(P))

    # Apply R(theta) to the quantum circuit
    qc.compose(R(theta), inplace=True)

    return qc
'''


'''python
from qiskit import QuantumCircuit
def solve(n: int, P: float, U, R) -> QuantumCircuit:
  qc = QuantumCircuit(n)
  for i in range(100):
    qc.compose(U(), inplace=True)
    qc.compose(R(1), inplace=True)
  return qc
'''


'''python
from qiskit import QuantumCircuit
import math
def solve(n: int, P: float, U, R) -> QuantumCircuit:
  qc = QuantumCircuit(n)
  for i in range(50):
    qc.compose(U(), inplace=True)
    qc.compose(R(math.pi), inplace=True)
    qc.compose(U().inverse(), inplace=True)
    qc.compose(R(math.pi).inverse(), inplace=True)
  return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    from math import acos, sqrt, pi
    theta = 2 * acos(sqrt(P))

    # Compute the inverse theta
    qc.compose(R(theta).inverse(), inplace=True)

    # Apply U inverse
    qc.compose(U().inverse(), inplace=True)

    # Apply R(theta) again
    qc.compose(R(theta), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np
"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    num_iterations = 10  # Adjust as needed

    # Initial application of U
    qc.compose(U(), inplace=True)

    # Amplitude amplification loop
    for _ in range(num_iterations):
        qc.compose(R(np.pi/2), inplace=True)  # Assuming optimal theta
        qc.compose(U().inverse(), inplace=True)
        qc.compose(R(np.pi/2), inplace=True)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range (100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range (100):
        qc.compose(R(math.pi / 3), inplace=True)
        #qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range (100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range (100):
        qc.compose(R(math.pi / 3), inplace=True)
        #qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    #for i in range(100):
    #    qc.compose(R(math.pi / 3), inplace=True)
    #    qc.compose(U().inverse(), inplace=True)
    #    for j in range(n):
    #        qc.x(j)
    #    qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
    #    for j in range(n):
    #        qc.x(j)
    #    qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U().replace(operation=U().operation.inverse(annotated=annotated)), inplace=True)
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc2 = QuantumCircuit(n)
        qc2.compose(U(), inplace=True)
        qc.append(qc2.inverse(), range(n))
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U(), inplace=True)
        for j in range(n):
            qc.x(j)
        qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(math.pi / 3, 0)
        else:
            qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(inverse(U()), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(math.pi / 3, 0)
        else:
            qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U.inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(math.pi / 3, 0)
        else:
            qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(inverse(U), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(math.pi / 3, 0)
        else:
            qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)

    for i in range(100):
        qc.compose(R(math.pi / 3), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(math.pi / 3, 0)
        else:
            qc.append(PhaseGate(math.pi / 3).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(1/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(np.cos((1/L)*np.arccos(1/delta)))
    l = (L-1)/2
    alpha=[]
    beta=[]
    for i in range(l):
        alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))

    for i in range(l):
        qc.compose(R(alpha[l-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(1/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(np.cos((1/L)*np.arccos(1/delta)))
    l = int(np.log(1/delta)/np.sqrt(P)/2)
    alpha=[]
    beta=[]
    for i in range(l):
        alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))

    for i in range(l):
        qc.compose(R(alpha[l-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(1/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(np.cos((1/L)*np.arccos(1/delta)))
    l = int(np.log(1/delta)/np.sqrt(P)/2)
    alpha=[]
    for i in range(l):
        alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))

    for i in range(l):
        qc.compose(R(-alpha[l-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(-alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(2/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(1-(np.log(1/delta)/L)**2)
    l = int(np.log(2/delta)/np.sqrt(P)/2)
    alpha=[]
    for i in range(l):
        alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))

    for i in range(l):
        qc.compose(R(-alpha[l-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(-alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(2/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(1-(np.log(1/delta)/L)**2)
    l = int(np.log(2/delta)/np.sqrt(P)/2)
    alpha=[]
    for i in range(l):
        #alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))
        alpha.append(np.pi/3)

    for i in range(l):
        qc.compose(R(-alpha[l-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(-alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(2/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(1-(np.log(1/delta)/L)**2)
    l = int(np.log(2/delta)/np.sqrt(P)/2)
    alpha=[]
    for i in range(100):
        #alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))
        alpha.append(np.pi/)

    for i in range(100):
        qc.compose(R(-alpha[l-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(-alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(2/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(1-(np.log(1/delta)/L)**2)
    l = int(np.log(2/delta)/np.sqrt(P)/2)
    alpha=[]
    for i in range(100):
        #alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))
        alpha.append(np.pi/)

    for i in range(100):
        qc.compose(R(-alpha[100-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(-alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import PhaseGate
import math
import numpy as np

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    delta=0.1
    L=int(np.log(2/delta)/np.sqrt(P)/2)*2 + 1
    gamma = 1/(1-(np.log(1/delta)/L)**2)
    l = int(np.log(2/delta)/np.sqrt(P)/2)
    alpha=[]
    for i in range(100):
        #alpha.append(2*np.arctan(1/(np.tan(i*np.pi*2/L)*np.sqrt(1-gamma**2))))
        alpha.append(np.pi/3)

    for i in range(100):
        qc.compose(R(-alpha[100-i-1]), inplace=True)
        qc.compose(U().inverse(), inplace=True)
        for j in range(n):
            qc.x(j)
        if(n==1):
            qc.p(alpha[i], 0)
        else:
            qc.append(PhaseGate(-alpha[i]).control(n - 1), range(n))
        for j in range(n):
            qc.x(j)
        qc.compose(U(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.append(U, range(n))

    # Define the phase gate R(θ) in terms of RZ and I
    # Note: This example assumes R(θ) has a known structure. You might need to adapt it to your specific case.
    def R(theta):
        # R(theta) = I - (1 - e^iθ) |ω⟩⟨ω|
        # Assume ω is the state after applying U
        # In the ideal case, we would need to apply RZ or other gates based on θ
        qc.rz(theta, 0)  # Example phase gate

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.append(U, range(n))
    def R(theta):
        qc.rz(theta, 0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.append(U, range(n))

    # Define the phase gate R(θ) in terms of RZ and I
    # Note: This example assumes R(θ) has a known structure. You might need to adapt it to your specific case.
    def R(theta):
         R(theta) = I - (1 - e^iθ) |ω⟩⟨ω|
        # Assume ω is the state after applying U
        # In the ideal case, we would need to apply RZ or other gates based on θ
        qc.rz(theta, 0)  # Example phase gate
        return qc

    # Apply R(θ) to the circuit
    qc = R(theta)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.append(U, range(n))
    def R(theta):
         R(theta) = I - (1 - e^iθ) |ω⟩⟨ω|
    qc = R(theta)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.append(U, range(n))
    def R(theta):
         R(theta) = I - (1 - e^i(theta)) |ω⟩⟨ω|
    qc = R(theta)
    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.append(U, range(n))

    def R(theta):
         R(theta) = I - (1 - e^i(theta)) |ω⟩⟨ω|
    qc.append(R(theta), range(n))
    return qc
'''


'''python
import math
from qiskit import QuantumCircuit

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Step 1: Prepare initial state using U
    qc.compose(U(), inplace=True)

    # If initial probability is already high enough, return the circuit as is
    if P >= 0.99:
        return qc

    # Step 2: Calculate the initial angle and determine rotation counts
    theta0 = math.asin(math.sqrt(P))             # initial angle such that sin^2(theta0) = P
    # Determine the number of full rotations without overshooting π/2
    if theta0 == 0:
        k_full = 0
    else:
        k_full = math.floor((math.pi/2 - theta0) / (2 * theta0))
    # Compute the angle achieved after k_full full rotations
    achieved_angle = (2 * k_full + 1) * theta0
    # Compute the partial rotation needed to reach π/2 (optimal) from achieved_angle
    theta_partial = (math.pi/2) - achieved_angle

    # Step 3: Apply k_full full R rotations
    full_rotation_angle = 2 * theta0  # angle for one full Grover iteration
    for _ in range(k_full):
        qc.compose(R(full_rotation_angle), inplace=True)

    # Step 4: Apply a partial rotation if needed to reach >= 99% success
    if theta_partial > 1e-6:  # if a significant partial rotation remains
        qc.compose(R(2 * theta_partial), inplace=True)
        # Note: If R(θ) is defined to perform a rotation by θ directly,
        # we should use R(theta_partial) here instead of R(2*theta_partial).
        # The factor 2 accounts for the typical Grover double-angle per iteration.

    return qc
'''


'''python
import math
from qiskit import QuantumCircuit

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # 初期状態の準備: U を適用
    qc.compose(U(), inplace=True)

    # 初期成功確率 P のアークサインを計算
    theta0 = math.asin(math.sqrt(P))

    # 固定点量子探索 (Grover-Yoder) の適用回数を決定
    k_max = min(100, math.ceil(math.log(1 / (1 - 0.99)) / math.log(3)))  # 保守的に100以下に制限

    # Grover-Yoder 法の位相シフトを適用
    for k in range(1, k_max + 1):
        theta_k = math.pi / (2 * k + 2)  # 位相シフト
        qc.compose(R(2 * theta_k), inplace=True)

    return qc
'''


'''python
import math
from qiskit import QuantumCircuit

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # 初期状態の準備: U を適用
    qc.compose(U(), inplace=True)

    # 初期角度 theta_0 の計算
    theta_k = math.asin(math.sqrt(P))

    # FPQS の適用回数の決定 (最大 100 ステップ)
    k_max = min(100, math.ceil(math.log(1 / (1 - 0.99)) / math.log(3)))

    for k in range(1, k_max + 1):
        # Grover-Yoder の適切な角度更新
        theta_k = math.atan( math.sin(theta_k) / (math.cos(theta_k) + 1 / math.tan(theta_k)) )

        # 量子回路に FPQS ステップを適用
        qc.compose(R(2 * theta_k), inplace=True)  # ターゲット状態の位相回転
        qc.compose(U().inverse(), inplace=True)   # 逆変換
        qc.compose(R(-2 * theta_k), inplace=True) # 逆位相回転
        qc.compose(U(), inplace=True)             # もう一度 U を適用

    return qc
'''


'''python
import math
from qiskit import QuantumCircuit

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # 初期状態の準備: U を適用
    qc.compose(U(), inplace=True)

    # 初期角度 theta_0 の計算
    theta_k = math.asin(math.sqrt(P))

    # 固定点量子探索の最大反復回数
    max_iterations = 100

    for k in range(max_iterations):
        # 現在の角度 theta_k に基づいて R(2 * theta_k) を適用
        qc.compose(R(2 * theta_k), inplace=True)
        # U の逆ゲートを適用
        qc.compose(U().inverse(), inplace=True)
        # R(-2 * theta_k) を適用
        qc.compose(R(-2 * theta_k), inplace=True)
        # U を再度適用
        qc.compose(U(), inplace=True)

        # 次の角度 theta_{k+1} を計算
        theta_k = 2 * math.asin(math.sin(theta_k / 2))

    return qc
'''


'''python
import math
from qiskit import QuantumCircuit

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)

    # 初期状態の準備: U を適用
    qc.compose(U(), inplace=True)

    # 初期角度 theta_0 の計算
    theta_k = math.asin(math.sqrt(P))

    # 固定点量子探索の最大反復回数
    max_iterations = 30

    for k in range(max_iterations):
        # 現在の角度 theta_k に基づいて R(2 * theta_k) を適用
        qc.compose(R(2 * theta_k), inplace=True)
        # U の逆ゲートを適用
        qc.compose(U().inverse(), inplace=True)
        # R(-2 * theta_k) を適用
        qc.compose(R(-2 * theta_k), inplace=True)
        # U を再度適用
        qc.compose(U(), inplace=True)

        # 次の角度 theta_{k+1} を計算
        theta_k = 2 * math.asin(math.sin(theta_k / 2))

    return qc
'''


'''python
from qiskit import QuantumCircuit

"""
You can apply U and R as follows:
qc.compose(U(), inplace=True)
qc.compose(R(theta), inplace=True)
"""

def solve(n: int, P: float, U, R) -> QuantumCircuit:
    qc = QuantumCircuit(n)
    # Write your code here:
    qc.compose(U(), inplace=True)
    qc.compose(R(theta), inplace=True)
    qc.compose(U().inverse(), inplace=True)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.global_phase += math.pi/2

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.s(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.z(0)
    qc.y(0)
    qc.x(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)

    qc.rz(math.pi, 0)
    qc.ry(math.pi, 0)

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)

    qc.rz(-math.pi, 0)
    qc.ry(math.pi, 0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.Y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.s(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.append(GlobalPhaseGate(math.pi / 2))

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library import GlobalPhaseGate
import numpy as np
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.append(GlobalPhaseGate(math.pi / 2))
    qc.x(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.circuit.library import YGate

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.append(YGate(), [0])

    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.h(0)
    qc.p(math.pi / 2, -0)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.p(math.pi/2, 0)
    return qc

# if __name__ == "__main__":
#     qc = solve()
#     print(Statevector(qc))
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.p(math.pi/2, 0)
    return qc

# if __name__ == "__main__":
#     qc = solve()
#     print(Statevector(qc))
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.p(math.pi/2, 0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Apply the S gate to the |1> state
    qc.x(0)  # First, we need to flip |0> to |1>
    qc.s(0)  # Apply the S gate to introduce the phase
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)#at 0
    qc.h(0)#|->
    qc.s(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.x(0)
    qc.z(0)
    # Write your code here:

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit
from math import pi

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.rx(3*pi, 0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.s(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import math

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    theta = math.pi/2
    qc.x(0)
    qc.p(theta, 0)

    return qc
'''


'''python
from glskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.x(0)
    qc.s(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.x(0)
    qc.s(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.h(0)
    qc.y(0)
    qc.h(0)
    qc.x(0)

    return qc
'''


'''python
import numpy as np
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    qc.y(0)
    return qc

if __name__ == '__main__':
    qc = solve()
    print(qc)
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.p(np.pi/2)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.p(np.pi/2)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.rz(np.pi/2)
    return qc
'''


'''python
from qiskit import QuantumCircuit
import numpy as np

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.s(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.x(0)
    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
    qc.y(0)
    return qc
'''


'''python
from qiskit import QuantumCircuit

def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:

    qc.y(0)

    return qc
'''


'''python
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.quantum_info import Statevector
from qiskit.circuit.library import ZGate
from math import sqrt, acos, pi

def solve():
	qc = QuantumCircuit(1)
	qc.y(0)
	return qc
'''