Alex is repairing his country house. He has a rectangular metal sheet of size a × b. He has to cut two rectangular sheets of sizes a1 × b1 and a2 × b2 from it. All cuts must be parallel to the sides of the initial sheet. Determine if he can do it.
The first line contains two space-separated integers a and b (1 ≤ a, b ≤ 109) — the sizes of the initial sheet.
The second line contains two space-separated integers a1 and b1 (1 ≤ a1, b1 ≤ 109) — the sizes of the first sheet to cut out.
The third line contains two space-separated integers a2 and b2 (1 ≤ a2, b2 ≤ 109) — the sizes of the second sheet to cut out.
Output «_YES_» (without quotes), if it's possible to cut two described sheets from the initial sheet, or «_NO_» (without quotes), if it's not possible.
## Input
The first line contains two space-separated integers a and b (1 ≤ a, b ≤ 109) — the sizes of the initial sheet.The second line contains two space-separated integers a1 and b1 (1 ≤ a1, b1 ≤ 109) — the sizes of the first sheet to cut out.The third line contains two space-separated integers a2 and b2 (1 ≤ a2, b2 ≤ 109) — the sizes of the second sheet to cut out.
## Output
Output «_YES_» (without quotes), if it's possible to cut two described sheets from the initial sheet, or «_NO_» (without quotes), if it's not possible.
[samples]
**Definitions**
Let $ a, b \in \mathbb{Z}^+ $ be the dimensions of the initial rectangular sheet.
Let $ (a_1, b_1), (a_2, b_2) \in \mathbb{Z}^+ \times \mathbb{Z}^+ $ be the dimensions of the two target rectangles.
For each target rectangle, rotation is allowed: i.e., $ (a_i, b_i) $ may be used as $ (b_i, a_i) $.
**Constraints**
1. $ 1 \leq a, b \leq 10^9 $
2. $ 1 \leq a_1, b_1, a_2, b_2 \leq 10^9 $
**Objective**
Determine whether there exist orientations $ o_1, o_2 \in \{0, 1\} $ such that the two rectangles
$ R_1 = (a_1^{o_1}, b_1^{o_1}) $ and $ R_2 = (a_2^{o_2}, b_2^{o_2}) $,
where
$$
x^0 = x, \quad x^1 = y, \quad y^0 = y, \quad y^1 = x
$$
can be placed non-overlappingly and entirely within the $ a \times b $ rectangle, with sides parallel to the axes.
That is, determine if there exists a way to partition the $ a \times b $ rectangle (via axis-aligned placement) to contain both $ R_1 $ and $ R_2 $ without overlap.
**Feasibility Conditions**
Define the set of possible orientations:
- $ O_1 = \{ (a_1, b_1), (b_1, a_1) \} $
- $ O_2 = \{ (a_2, b_2), (b_2, a_2) \} $
Then, output "YES" if there exist $ (w_1, h_1) \in O_1 $, $ (w_2, h_2) \in O_2 $, such that **at least one** of the following holds:
1. **Side-by-side horizontally**:
$ w_1 + w_2 \leq a $ and $ \max(h_1, h_2) \leq b $
2. **Stacked vertically**:
$ h_1 + h_2 \leq b $ and $ \max(w_1, w_2) \leq a $
3. **L-shaped (w1 + w2 ≤ a, h1 + h2 ≤ b, with one placed beside and above the other)**:
$ w_1 + w_2 \leq a $ and $ h_1 + h_2 \leq b $ and $ w_1 \leq a $, $ w_2 \leq a $, $ h_1 \leq b $, $ h_2 \leq b $
*(Note: This is implied by the above two if we allow arbitrary placement; however, in axis-aligned non-overlapping packing of two rectangles into a bounding rectangle, the only viable configurations are side-by-side, stacked, or one placed beside and above — which reduces to checking the two above plus two more:)*
Actually, to be complete, also check:
4. $ w_1 + h_2 \leq a $ and $ h_1 + w_2 \leq b $ (one rotated to fit beside and above)
5. $ w_2 + h_1 \leq a $ and $ h_2 + w_1 \leq b $
But the standard and sufficient approach is to check all 4 combinations of orientations, and for each, check:
- Horizontal arrangement: $ w_1 + w_2 \leq a $ and $ \max(h_1, h_2) \leq b $
- Vertical arrangement: $ h_1 + h_2 \leq b $ and $ \max(w_1, w_2) \leq a $
- “L”-shaped: $ w_1 + w_2 \leq a $ and $ h_1 + h_2 \leq b $ — **but this is NOT sufficient alone**
Actually, the **correct and complete set** of configurations to check for two rectangles in a bounding rectangle is:
For each $ (w_1, h_1) \in O_1 $, $ (w_2, h_2) \in O_2 $:
- **Side-by-side**: $ w_1 + w_2 \leq a $ and $ h_1 \leq b $ and $ h_2 \leq b $ and $ \max(h_1, h_2) \leq b $
- **Stacked**: $ h_1 + h_2 \leq b $ and $ w_1 \leq a $ and $ w_2 \leq a $ and $ \max(w_1, w_2) \leq a $
- **One beside, one above (L-shape)**:
- $ w_1 + w_2 \leq a $ and $ h_1 + h_2 \leq b $
- **AND** $ w_1 \leq a $, $ w_2 \leq a $, $ h_1 \leq b $, $ h_2 \leq b $ — always true if above holds
But the L-shape requires:
Either:
- $ w_1 + w_2 \leq a $ and $ h_1 + h_2 \leq b $
(This allows placing one rectangle to the right of the other, and one above the other — but only if they are arranged in an L, meaning one is placed in corner, the other in adjacent corner — which is valid if the bounding box is $ \max(w_1, w_2) \times \max(h_1, h_2) $, which is **not** the case)
Actually, **the only two valid configurations** are:
- **Horizontal**: total width $ w_1 + w_2 \leq a $, height $ \max(h_1, h_2) \leq b $
- **Vertical**: total height $ h_1 + h_2 \leq b $, width $ \max(w_1, w_2) \leq a $
- **Mixed (L-shape)**:
- $ w_1 + h_2 \leq a $ and $ h_1 + w_2 \leq b $
- $ w_2 + h_1 \leq a $ and $ h_2 + w_1 \leq b $
So in total, for each of the 4 orientation pairs, check:
1. $ w_1 + w_2 \leq a $ and $ \max(h_1, h_2) \leq b $
2. $ h_1 + h_2 \leq b $ and $ \max(w_1, w_2) \leq a $
3. $ w_1 + h_2 \leq a $ and $ h_1 + w_2 \leq b $
4. $ w_2 + h_1 \leq a $ and $ h_2 + w_1 \leq b $
But (3) and (4) are redundant if we consider all 4 orientation combinations — since $ (w_1, h_1) $ and $ (w_2, h_2) $ already include both orientations.
Thus, simply iterate over all 4 combinations of orientations, and for each, check:
- $ w_1 + w_2 \leq a $ and $ \max(h_1, h_2) \leq b $
- $ h_1 + h_2 \leq b $ and $ \max(w_1, w_2) \leq a $
**Final Objective**
$$
\exists \, (w_1, h_1) \in \{(a_1, b_1), (b_1, a_1)\}, \quad (w_2, h_2) \in \{(a_2, b_2), (b_2, a_2)\}
$$
such that
$$
(w_1 + w_2 \leq a \land \max(h_1, h_2) \leq b) \quad \lor \quad (h_1 + h_2 \leq b \land \max(w_1, w_2) \leq a)
$$
Output "YES" if true, "NO" otherwise.