Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np


def solve(s):
    n = len(s)
    size = n // 2
    MOD = 998244353
    dp_can = np.zeros((n + 1, size + 1, size + 1), dtype=np.int8)
    dp_cnt = np.zeros((n + 1, size + 1, size + 1), dtype=np.int64)

    dp_cnt[n, 0] = 1
    for j in range(size):
        dp_cnt[n, j + 1] = np.cumsum(dp_cnt[n, j]) % MOD

    for i in range(n - 1, -1, -1):
        if s[i] == '0':
            dp_cnt[i] = np.cumsum(dp_cnt[i + 1], axis=1) % MOD
        else:
            dp_cnt[i] = np.cumsum(dp_cnt[i + 1], axis=0) % MOD

    dp_can[0, 0, 0] = 1
    for i in range(n):
        dp_can[i + 1] |= dp_can[i]
        if s[i] == '0':
            dp_can[i + 1, 1:, :-1] |= dp_can[i, :-1, 1:]
        else:
            dp_can[i + 1, :-1, 1:] |= dp_can[i, 1:, :-1]
        if i < n - 1:
            if s[i] == '0' or s[i + 1] == '0':
                dp_can[i + 2, 1:, :] |= dp_can[i, :-1, :]
            if s[i] == '1' or s[i + 1] == '1':
                dp_can[i + 2, :, 1:] |= dp_can[i, :, :-1]
    dp_can[1:, 0, 0] = 0

    ans = 0

    for i in range(n, -1, -1):
        for j in range(size + 1):
            for k in range(size + 1):
                if dp_can[i, j, k] == 0:
                    continue

                ans = (ans + dp_cnt[i, j, k]) % MOD

                a, b = j, k
                for h in range(i - 1, -1, -1):
                    if s[h] == '0':
                        a -= 1
                    else:
                        b -= 1
                    if a < 0 or b < 0:
                        break
                    dp_can[h, a, b] = 0

    return ans


s = input()
ans = solve(s)
print(ans)


Fixed submission:
import numpy as np
import numba as nb


@nb.njit('(i1[:],)', cache=True)
def solve(s):
    n = len(s)
    size = n // 2
    MOD = 998244353
    dp_can = np.zeros((n + 1, size + 1, size + 1), dtype=np.int8)
    dp_cnt = np.zeros((n + 1, size + 1, size + 1), dtype=np.int64)

    dp_cnt[n, 0] = 1
    for j in range(size):
        dp_cnt[n, j + 1] = np.cumsum(dp_cnt[n, j]) % MOD

    for i in range(n - 1, -1, -1):
        if s[i] == 0:
            for j in range(size + 1):
                dp_cnt[i, j] = np.cumsum(dp_cnt[i + 1, j]) % MOD
        else:
            for k in range(size + 1):
                dp_cnt[i, :, k] = np.cumsum(dp_cnt[i + 1, :, k]) % MOD

    dp_can[0, 0, 0] = 1
    for i in range(n):
        dp_can[i + 1] |= dp_can[i]
        if s[i] == 0:
            dp_can[i + 1, 1:, :-1] |= dp_can[i, :-1, 1:]
        else:
            dp_can[i + 1, :-1, 1:] |= dp_can[i, 1:, :-1]
        if i < n - 1:
            if s[i] == 0 or s[i + 1] == 0:
                dp_can[i + 2, 1:, :] |= dp_can[i, :-1, :]
            if s[i] == 1 or s[i + 1] == 1:
                dp_can[i + 2, :, 1:] |= dp_can[i, :, :-1]
    dp_can[1:, 0, 0] = 0

    ans = 0

    for i in range(n, -1, -1):
        for j in range(size + 1):
            for k in range(size + 1):
                if dp_can[i, j, k] == 0:
                    continue

                ans = (ans + dp_cnt[i, j, k]) % MOD

                a, b = j, k
                for h in range(i - 1, -1, -1):
                    if s[h] == 0:
                        a -= 1
                    else:
                        b -= 1
                    if a < 0 or b < 0:
                        break
                    dp_can[h, a, b] = 0

    return ans


s = np.array([int(c) for c in input()], dtype=np.int8)
print(solve(s))