Problem: Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.

Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.

Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?

Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:

* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z



Since the answer can be extremely large, print the number modulo 10^9+7.

Constraints

* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5

Input

The input is given from Standard Input in the following format:


N X Y Z


Output

Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.

Examples

Input

3 5 7 5


Output

1


Input

4 5 7 5


Output

34


Input

37 4 2 3


Output

863912418


Input

40 5 7 5


Output

562805100

Solution (in PYTHON3):

Solution:
# seishin.py
N, X, Y, Z = map(int, input().split())
m = 2**(X+Y+Z)
S = [0]*m

L = max(X, Y, Z)

ss = set()
tt = set()

Z0 = (1 << (Z-1))
Y0 = (1 << (Z+Y-1))
X0 = (1 << (X+Z+Y-1))

for i in range(m):
    if i & Z0 and i & Y0 and i & X0:
        ss.add(i)

MASK = 2**(X+Y+Z)-1
MOD = 10**9 + 7

S[0] = 1
for i in range(N):
    T = [0]*m
    for s in range(m):
        if s in ss:
            # XYZが成立
            continue
        b = (s << 1) | 1
        for k in range(1, L+1):
            t = (b << (k-1)) & MASK
            T[t] = (T[t] + S[s]) % MOD
        for k in range(L+1, 11):
            T[0] = (T[0] + S[s]) % MOD
    S = T
ans = 0
for s in range(m):
    if s in ss:
        continue
    ans = (ans + S[s]) % MOD
ans = (pow(10, N, MOD) + MOD - ans) % MOD
print(ans)