Ayoub had an array a of integers of size n and this array had two interesting properties: 

  * All the integers in the array were between l and r (inclusive). 
  * The sum of all the elements was divisible by 3. 



Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array. 

Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.

Input

The first and only line contains three integers n, l and r (1 ≤ n ≤ 2 ⋅ 10^5 , 1 ≤ l ≤ r ≤ 10^9) — the size of the lost array and the range of numbers in the array.

Output

Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.

Examples

Input


2 1 3


Output


3


Input


3 2 2


Output


1


Input


9 9 99


Output


711426616

Note

In the first example, the possible arrays are : [1,2], [2,1], [3, 3].

In the second example, the only possible array is [2, 2, 2].
#!/usr/bin/env python
# coding: utf-8

# In[22]:


stuff=list(map(int, input().rstrip().split()))


# In[23]:


n=stuff[0]
l=stuff[1]
r=stuff[2]

mod=10**9+7


# In[24]:



zeromods=r//3-(l-1)//3

onemods=(r-1)//3-(l-2)//3

twomods=(r-2)//3-(l-3)//3


# In[25]:


combos=[[0,0,0] for i in range(n)]


# In[26]:


combos[0]=[zeromods,onemods,twomods]


# In[28]:


for i in range(1,n):
    combos[i][0]=(combos[i-1][0]*zeromods+combos[i-1][1]*twomods+combos[i-1][2]*onemods)%mod 
    
    
    combos[i][1]=(combos[i-1][0]*onemods+combos[i-1][1]*zeromods+combos[i-1][2]*twomods)%mod
    
    
    combos[i][2]=(combos[i-1][0]*twomods+combos[i-1][1]*onemods+combos[i-1][2]*zeromods)%mod 
    
    
    
print(combos[-1][0])    


# In[29]:


combos


# In[ ]:




